Subgroups — C₁₉×#18995 #18024954

Order 4864.

1024 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3529	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3217	C₂	1	2	yes	maximal, complemented
3	C₁₉×#3151	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1657	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1656	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1655	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1536	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1529	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₉×AGL(1,ℤ/8)	—	2	1	no	—
10	C₂×C₁₉×AGL(1,ℤ/8)	—	2	1	no	—
11	C₁₉×#563	—	2	1	no	—
12	C₁₉×#563	C₂²	1	1	yes	characteristic, complemented
13	C₁₉×#562	—	2	2	no	—
14	C₁₉×#562	C₂²	1	2	yes	complemented
15	C₁₉×H(3,𝔽₄)	C₂²	1	1	yes	characteristic, complemented
16	C₁₉×#560	—	2	1	no	—
17	C₁₉×#560	—	2	2	no	—
18	C₁₉×#532	—	2	1	no	—
19	C₁₉×#532	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic, complemented
21	C₁₉×#529	—	2	2	no	—
22	C₁₉×#529	C₂²	1	2	yes	—
23	C₁₉×#525	—	2	1	no	—
24	C₁₉×#525	—	2	2	no	—
25	C₁₉×#496	C₂²	1	4	yes	—
26	C₁₉×#496	C₂²	1	2	yes	—
27	C₁₉×#496	C₂²	1	2	yes	complemented
28	C₁₉×#493	—	2	1	no	—
29	C₁₉×#492	—	2	1	no	—
30	C₁₉×#490	C₂²	1	4	yes	complemented
31	C₁₉×#460	—	2	2	no	—
32	C₁₉×#459	—	2	2	no	—
33	C₁₉×#450	—	2	2	no	—
34	C₁₉×#447	—	2	2	no	—
35	C₁₉×#432	C₂²	1	2	yes	complemented
36	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
37	C₁₉×#330	C₂²	1	4	yes	complemented
38	C₁₉×#329	C₂²	1	4	yes	complemented
39	C₁₉×#329	C₂²	1	2	yes	complemented
40	C₁₉×#329	C₂²	1	2	yes	complemented
41	C₂×#41×C₁₉	—	2	1	no	—
42	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
43	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
44	C₂²×D₄×C₁₉	—	2	1	no	—
45	C₂²×D₄×C₁₉	—	2	2	no	—
46	C₂³×C₄×C₁₉	—	2	1	no	—
47	C₁₉×AGL(1,ℤ/8)	—	4	4	no	—
48	C₁₉×AGL(1,ℤ/8)	—	4	4	no	—
49	C₂×SD₁₆×C₁₉	—	2	2	no	—
50	C₂×SD₁₆×C₁₉	—	2	2	no	—
51	C₂×SD₁₆×C₁₉	—	2	4	no	—
52	C₂×D₈×C₁₉	—	2	2	no	—
53	C₂×D₈×C₁₉	—	2	2	no	—
54	C₂×D₈×C₁₉	—	2	4	no	—
55	C₂×M₁₆×C₁₉	—	2	1	no	—
56	C₁₉×C₄⋊Q₈	—	2	1	no	—
57	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
58	C₁₉×#127	—	2	1	no	—
59	C₁₉×#127	—	2	2	no	—
60	C₁₉×#127	—	2	1	no	—
61	C₁₉×#127	D₄	1	1	yes	characteristic
62	C₁₉×#127	C₂³	1	2	yes	—
63	C₁₉×#126	—	2	2	no	—
64	C₁₉×#126	—	2	2	no	—
65	C₁₉×#126	—	2	2	no	—
66	C₁₉×#125	—	2	2	no	—
67	C₁₉×#125	C₂³	1	2	yes	—
68	C₁₉×#124	—	2	1	no	—
69	C₁₉×#124	—	2	2	no	—
70	C₁₉×#124	—	2	1	no	—
71	C₁₉×#124	C₂³	1	2	yes	—
72	C₁₉×#124	C₂³	1	1	yes	characteristic
73	C₁₉×#124	C₂³	1	1	yes	characteristic
74	C₁₉×#123	—	2	2	no	—
75	C₁₉×#123	—	2	1	no	—
76	C₁₉×#123	—	2	2	no	—
77	C₁₉×#123	—	2	1	no	—
78	C₁₉×#123	—	2	2	no	—
79	C₁₉×#123	—	2	2	no	—
80	C₁₉×#123	—	2	2	no	—
81	C₁₉×C₂²⋊Q₈	—	2	2	no	—
82	C₁₉×C₂²⋊Q₈	—	2	2	no	—
83	C₁₉×C₂²⋊Q₈	—	2	2	no	—
84	C₁₉×C₂²⋊Q₈	—	2	2	no	—
85	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
86	C₁₉×#121	—	2	2	no	—
87	C₁₉×#121	—	2	2	no	—
88	C₁₉×#121	—	2	2	no	—
89	C₁₉×#121	—	2	2	no	—
90	C₁₉×#121	—	2	2	no	—
91	C₁₉×#121	—	2	2	no	—
92	C₁₉×#121	—	2	2	no	—
93	C₁₉×#121	D₄	1	2	yes	—
94	C₁₉×#120	—	2	1	no	—
95	C₁₉×#120	—	2	2	no	—
96	C₁₉×#120	—	2	1	no	—
97	C₁₉×#120	—	2	2	no	—
98	C₄×Q₈×C₁₉	D₄	1	2	yes	—
99	C₄×D₄×C₁₉	—	2	2	no	—
100	C₄×D₄×C₁₉	—	2	2	no	—
101	C₄×D₄×C₁₉	—	2	2	no	—
102	C₄×D₄×C₁₉	—	2	2	no	—
103	C₄×D₄×C₁₉	D₄	1	2	yes	—
104	C₁₉×#117	—	2	1	no	—
105	C₁₉×#117	—	2	2	no	—
106	C₂×C₄²×C₁₉	—	2	1	no	—
107	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
108	C₁₉×C₄⋊C₈	—	2	2	no	—
109	C₁₉×#102	—	2	4	no	—
110	C₁₉×#102	—	2	4	no	—
111	C₁₉×C₂²⋊C₈	—	2	2	no	—
112	C₁₉×#97	C₂³	1	2	yes	—
113	C₁₉×#97	C₂³	1	4	yes	—
114	C₄×C₈×C₁₉	—	2	1	no	—
115	C₂⁴×C₁₉	—	2	1	no	—
116	C₂⁴×C₁₉	—	4	1	no	—
117	#41×C₁₉	—	4	2	no	—
118	#41×C₁₉	—	4	2	no	—
119	#41×C₁₉	—	8	2	no	—
120	C₂×Q₈×C₁₉	—	2	1	no	—
121	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
122	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
123	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
124	C₂×D₄×C₁₉	—	2	2	no	—
125	C₂×D₄×C₁₉	—	2	2	no	—
126	C₂×D₄×C₁₉	—	2	1	no	—
127	C₂×D₄×C₁₉	—	2	2	no	—
128	C₂×D₄×C₁₉	—	2	2	no	—
129	C₂×D₄×C₁₉	—	2	1	no	—
130	C₂×D₄×C₁₉	—	2	1	no	—
131	C₂×D₄×C₁₉	—	2	2	no	—
132	C₂×D₄×C₁₉	—	2	2	no	—
133	C₂×D₄×C₁₉	—	2	4	no	—
134	C₂×D₄×C₁₉	—	4	2	no	—
135	C₂×D₄×C₁₉	—	4	2	no	—
136	C₂×D₄×C₁₉	—	4	2	no	—
137	C₂×D₄×C₁₉	—	4	1	no	—
138	C₂×D₄×C₁₉	—	8	4	no	—
139	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
140	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
141	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₉	—	2	2	no	—
143	C₂²×C₄×C₁₉	—	2	2	no	—
144	C₂²×C₄×C₁₉	—	2	1	no	—
145	C₂²×C₄×C₁₉	—	2	1	no	—
146	C₂²×C₄×C₁₉	—	2	1	no	—
147	C₂²×C₄×C₁₉	—	2	2	no	—
148	C₂²×C₄×C₁₉	—	8	2	no	—
149	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
151	SD₁₆×C₁₉	—	4	4	no	—
152	SD₁₆×C₁₉	—	4	4	no	—
153	SD₁₆×C₁₉	—	8	4	no	—
154	D₈×C₁₉	—	4	4	no	—
155	D₈×C₁₉	—	4	4	no	—
156	D₈×C₁₉	—	8	4	no	—
157	M₁₆×C₁₉	—	2	4	no	—
158	C₂×C₈×C₁₉	—	2	2	no	—
159	C₂×C₈×C₁₉	—	2	4	no	—
160	C₄⋊C₄×C₁₉	—	2	2	no	—
161	C₄⋊C₄×C₁₉	—	2	2	no	—
162	C₄⋊C₄×C₁₉	—	2	2	no	—
163	C₄⋊C₄×C₁₉	—	2	2	no	—
164	C₄⋊C₄×C₁₉	—	2	2	no	—
165	C₄⋊C₄×C₁₉	—	2	2	no	—
166	C₄⋊C₄×C₁₉	—	2	2	no	—
167	C₄⋊C₄×C₁₉	—	2	2	no	—
168	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
169	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
170	C₂²⋊C₄×C₁₉	—	2	1	no	—
171	C₂²⋊C₄×C₁₉	—	2	1	no	—
172	C₂²⋊C₄×C₁₉	—	2	2	no	—
173	C₂²⋊C₄×C₁₉	—	2	2	no	—
174	C₂²⋊C₄×C₁₉	—	2	2	no	—
175	C₂²⋊C₄×C₁₉	—	2	2	no	—
176	C₂²⋊C₄×C₁₉	—	2	2	no	—
177	C₂²⋊C₄×C₁₉	—	2	2	no	—
178	C₂²⋊C₄×C₁₉	—	2	2	no	—
179	C₂²⋊C₄×C₁₉	—	2	2	no	—
180	C₂²⋊C₄×C₁₉	—	2	2	no	—
181	C₂²⋊C₄×C₁₉	—	2	2	no	—
182	C₂²⋊C₄×C₁₉	—	2	2	no	—
183	C₄²×C₁₉	—	2	1	no	—
184	C₄²×C₁₉	—	2	1	no	—
185	C₄²×C₁₉	—	2	2	no	—
186	C₄²×C₁₉	C₂×D₄	1	2	yes	—
187	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
188	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
189	#18995	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
190	C₂³×C₁₉	—	2	1	no	—
191	C₂³×C₁₉	—	2	2	no	—
192	C₂³×C₁₉	—	2	1	no	—
193	C₂³×C₁₉	—	4	2	no	—
194	C₂³×C₁₉	—	8	2	no	—
195	C₂³×C₁₉	—	8	4	no	—
196	C₂³×C₁₉	—	8	1	no	—
197	C₂³×C₁₉	—	8	2	no	—
198	C₂³×C₁₉	#120	1	1	yes	characteristic
199	Q₈×C₁₉	—	4	1	no	—
200	Q₈×C₁₉	—	4	1	no	—
201	Q₈×C₁₉	—	4	2	no	—
202	Q₈×C₁₉	—	8	1	no	—
203	D₄×C₁₉	—	4	1	no	—
204	D₄×C₁₉	—	4	1	no	—
205	D₄×C₁₉	—	4	2	no	—
206	D₄×C₁₉	—	4	2	no	—
207	D₄×C₁₉	—	4	2	no	—
208	D₄×C₁₉	—	4	4	no	—
209	D₄×C₁₉	—	4	4	no	—
210	D₄×C₁₉	—	8	2	no	—
211	D₄×C₁₉	—	8	4	no	—
212	D₄×C₁₉	—	8	2	no	—
213	D₄×C₁₉	—	8	1	no	—
214	D₄×C₁₉	—	8	1	no	—
215	D₄×C₁₉	—	8	2	no	—
216	D₄×C₁₉	—	8	2	no	—
217	D₄×C₁₉	—	8	2	no	—
218	D₄×C₁₉	—	8	1	no	—
219	D₄×C₁₉	—	8	2	no	—
220	C₂×C₄×C₁₉	—	2	2	no	—
221	C₂×C₄×C₁₉	—	2	2	no	—
222	C₂×C₄×C₁₉	—	2	2	no	—
223	C₂×C₄×C₁₉	—	2	1	no	—
224	C₂×C₄×C₁₉	—	2	1	no	—
225	C₂×C₄×C₁₉	—	2	2	no	—
226	C₂×C₄×C₁₉	—	4	2	no	—
227	C₂×C₄×C₁₉	—	4	2	no	—
228	C₂×C₄×C₁₉	—	4	4	no	—
229	C₂×C₄×C₁₉	—	4	2	no	—
230	C₂×C₄×C₁₉	—	8	2	no	—
231	C₂×C₄×C₁₉	—	8	2	no	—
232	C₂×C₄×C₁₉	—	8	1	no	—
233	C₂×C₄×C₁₉	#120	1	2	yes	—
234	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
235	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
236	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
237	C₈×C₁₉	—	2	4	no	—
238	C₈×C₁₉	—	4	4	no	—
239	#3529	C₂×C₁₉	1	1	yes	characteristic, complemented
240	#3217	C₂×C₁₉	1	2	yes	complemented
241	#3151	C₂×C₁₉	1	1	yes	characteristic, complemented
242	#1657	C₂×C₁₉	1	2	yes	complemented
243	#1656	C₂×C₁₉	1	4	yes	complemented
244	#1655	C₂×C₁₉	1	2	yes	complemented
245	#1536	C₂×C₁₉	1	1	yes	characteristic, complemented
246	#1529	C₂×C₁₉	1	2	yes	complemented
247	C₂²×C₁₉	—	2	1	no	—
248	C₂²×C₁₉	—	2	2	no	—
249	C₂²×C₁₉	—	4	1	no	—
250	C₂²×C₁₉	—	4	2	no	—
251	C₂²×C₁₉	—	4	1	no	—
252	C₂²×C₁₉	—	4	2	no	—
253	C₂²×C₁₉	—	4	2	no	—
254	C₂²×C₁₉	—	4	2	no	—
255	C₂²×C₁₉	—	4	2	no	—
256	C₂²×C₁₉	—	8	4	no	—
257	C₂²×C₁₉	—	8	2	no	—
258	C₂²×C₁₉	—	8	4	no	—
259	C₂²×C₁₉	—	16	4	no	—
260	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
261	C₄×C₁₉	—	2	1	no	—
262	C₄×C₁₉	—	2	2	no	—
263	C₄×C₁₉	—	2	2	no	—
264	C₄×C₁₉	—	4	1	no	—
265	C₄×C₁₉	—	4	2	no	—
266	C₄×C₁₉	—	4	1	no	—
267	C₄×C₁₉	—	4	2	no	—
268	C₄×C₁₉	—	4	2	no	—
269	C₄×C₁₉	#453	1	2	yes	—
270	C₂×AGL(1,ℤ/8)	—	2	1	no	—
271	C₂×AGL(1,ℤ/8)	—	2	1	no	—
272	#563	—	2	1	no	—
273	#563	C₂²×C₁₉	1	1	yes	characteristic, complemented
274	#562	—	2	2	no	—
275	#562	C₂²×C₁₉	1	2	yes	complemented
276	H(3,𝔽₄)	C₂²×C₁₉	1	1	yes	characteristic, complemented
277	#560	—	2	1	no	—
278	#560	—	2	2	no	—
279	#532	—	2	1	no	—
280	#532	C₂²×C₁₉	1	1	yes	characteristic
281	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic, complemented
282	#529	—	2	2	no	—
283	#529	C₂²×C₁₉	1	2	yes	—
284	#525	—	2	1	no	—
285	#525	—	2	2	no	—
286	#496	C₂²×C₁₉	1	2	yes	—
287	#496	C₂²×C₁₉	1	4	yes	—
288	#496	C₂²×C₁₉	1	2	yes	complemented
289	#493	—	2	1	no	—
290	#492	—	2	1	no	—
291	#490	C₂²×C₁₉	1	4	yes	complemented
292	#460	—	2	2	no	—
293	#459	—	2	2	no	—
294	#450	—	2	2	no	—
295	#447	—	2	2	no	—
296	#432	C₂²×C₁₉	1	2	yes	complemented
297	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
298	#330	C₂²×C₁₉	1	4	yes	complemented
299	#329	C₂²×C₁₉	1	2	yes	complemented
300	#329	C₂²×C₁₉	1	2	yes	complemented
301	#329	C₂²×C₁₉	1	4	yes	complemented
302	C₂×C₁₉	—	4	1	no	—
303	C₂×C₁₉	—	8	1	no	—
304	C₂×C₁₉	—	8	1	no	—
305	C₂×C₁₉	—	8	2	no	—
306	C₂×C₁₉	—	16	2	no	—
307	C₂×C₁₉	C₂×#453	1	1	yes	characteristic
308	C₂×C₁₉	#3021	1	2	yes	—
309	C₂×#41	—	2	1	no	—
310	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
311	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
312	C₂²×D₄	—	2	1	no	—
313	C₂²×D₄	—	2	2	no	—
314	C₂³×C₄	—	2	1	no	—
315	AGL(1,ℤ/8)	—	4	4	no	—
316	AGL(1,ℤ/8)	—	4	4	no	—
317	C₂×SD₁₆	—	2	2	no	—
318	C₂×SD₁₆	—	2	2	no	—
319	C₂×SD₁₆	—	2	4	no	—
320	C₂×D₈	—	2	2	no	—
321	C₂×D₈	—	2	2	no	—
322	C₂×D₈	—	2	4	no	—
323	C₂×M₁₆	—	2	1	no	—
324	C₄⋊Q₈	—	2	1	no	—
325	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
326	#127	—	2	1	no	—
327	#127	—	2	2	no	—
328	#127	—	2	1	no	—
329	#127	D₄×C₁₉	1	1	yes	characteristic
330	#127	C₂³×C₁₉	1	2	yes	—
331	#126	—	2	2	no	—
332	#126	—	2	2	no	—
333	#126	—	2	2	no	—
334	#125	—	2	2	no	—
335	#125	C₂³×C₁₉	1	2	yes	—
336	#124	—	2	1	no	—
337	#124	—	2	2	no	—
338	#124	—	2	1	no	—
339	#124	C₂³×C₁₉	1	2	yes	—
340	#124	C₂³×C₁₉	1	1	yes	characteristic
341	#124	C₂³×C₁₉	1	1	yes	characteristic
342	#123	—	2	2	no	—
343	#123	—	2	1	no	—
344	#123	—	2	2	no	—
345	#123	—	2	1	no	—
346	#123	—	2	2	no	—
347	#123	—	2	2	no	—
348	#123	—	2	2	no	—
349	C₂²⋊Q₈	—	2	2	no	—
350	C₂²⋊Q₈	—	2	2	no	—
351	C₂²⋊Q₈	—	2	2	no	—
352	C₂²⋊Q₈	—	2	2	no	—
353	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
354	#121	—	2	2	no	—
355	#121	—	2	2	no	—
356	#121	—	2	2	no	—
357	#121	—	2	2	no	—
358	#121	—	2	2	no	—
359	#121	—	2	2	no	—
360	#121	—	2	2	no	—
361	#121	D₄×C₁₉	1	2	yes	—
362	#120	—	2	1	no	—
363	#120	—	2	2	no	—
364	#120	—	2	1	no	—
365	#120	—	2	2	no	—
366	C₄×Q₈	D₄×C₁₉	1	2	yes	—
367	C₄×D₄	—	2	2	no	—
368	C₄×D₄	—	2	2	no	—
369	C₄×D₄	—	2	2	no	—
370	C₄×D₄	—	2	2	no	—
371	C₄×D₄	D₄×C₁₉	1	2	yes	—
372	#117	—	2	1	no	—
373	#117	—	2	2	no	—
374	C₂×C₄²	—	2	1	no	—
375	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
376	C₄⋊C₈	—	2	2	no	—
377	#102	—	2	4	no	—
378	#102	—	2	4	no	—
379	C₂²⋊C₈	—	2	2	no	—
380	#97	C₂³×C₁₉	1	4	yes	—
381	#97	C₂³×C₁₉	1	2	yes	—
382	C₄×C₈	—	2	1	no	—
383	C₁₉	#18995	1	1	yes	characteristic, direct product factor, Sylow
384	C₂⁴	—	2	1	no	—
385	C₂⁴	—	4	1	no	—
386	#41	—	4	2	no	—
387	#41	—	4	2	no	—
388	#41	—	8	2	no	—
389	C₂×Q₈	—	2	1	no	—
390	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
391	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
392	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
393	C₂×D₄	—	2	2	no	—
394	C₂×D₄	—	2	2	no	—
395	C₂×D₄	—	2	1	no	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	2	1	no	—
399	C₂×D₄	—	2	1	no	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	2	4	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	4	2	no	—
404	C₂×D₄	—	4	2	no	—
405	C₂×D₄	—	4	2	no	—
406	C₂×D₄	—	4	1	no	—
407	C₂×D₄	—	8	4	no	—
408	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
409	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
410	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	8	2	no	—
418	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
419	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
420	SD₁₆	—	4	4	no	—
421	SD₁₆	—	4	4	no	—
422	SD₁₆	—	8	4	no	—
423	D₈	—	4	4	no	—
424	D₈	—	4	4	no	—
425	D₈	—	8	4	no	—
426	M₁₆	—	2	4	no	—
427	C₂×C₈	—	2	2	no	—
428	C₂×C₈	—	2	4	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	2	2	no	—
433	C₄⋊C₄	—	2	2	no	—
434	C₄⋊C₄	—	2	2	no	—
435	C₄⋊C₄	—	2	2	no	—
436	C₄⋊C₄	—	2	2	no	—
437	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
438	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
439	C₂²⋊C₄	—	2	1	no	—
440	C₂²⋊C₄	—	2	1	no	—
441	C₂²⋊C₄	—	2	2	no	—
442	C₂²⋊C₄	—	2	2	no	—
443	C₂²⋊C₄	—	2	2	no	—
444	C₂²⋊C₄	—	2	2	no	—
445	C₂²⋊C₄	—	2	2	no	—
446	C₂²⋊C₄	—	2	2	no	—
447	C₂²⋊C₄	—	2	2	no	—
448	C₂²⋊C₄	—	2	2	no	—
449	C₂²⋊C₄	—	2	2	no	—
450	C₂²⋊C₄	—	2	2	no	—
451	C₂²⋊C₄	—	2	2	no	—
452	C₄²	—	2	1	no	—
453	C₄²	—	2	1	no	—
454	C₄²	—	2	2	no	—
455	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
456	C₄²	C₂×D₄×C₁₉	1	2	yes	—
457	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
458	C₂³	—	2	1	no	—
459	C₂³	—	2	2	no	—
460	C₂³	—	2	1	no	—
461	C₂³	—	4	2	no	—
462	C₂³	—	8	2	no	—
463	C₂³	—	8	4	no	—
464	C₂³	—	8	1	no	—
465	C₂³	—	8	2	no	—
466	C₂³	C₁₉×#120	1	1	yes	characteristic
467	Q₈	—	4	1	no	—
468	Q₈	—	4	1	no	—
469	Q₈	—	4	2	no	—
470	Q₈	—	8	1	no	—
471	D₄	—	4	1	no	—
472	D₄	—	4	1	no	—
473	D₄	—	4	2	no	—
474	D₄	—	4	2	no	—
475	D₄	—	4	2	no	—
476	D₄	—	4	4	no	—
477	D₄	—	4	4	no	—
478	D₄	—	8	2	no	—
479	D₄	—	8	4	no	—
480	D₄	—	8	1	no	—
481	D₄	—	8	1	no	—
482	D₄	—	8	2	no	—
483	D₄	—	8	2	no	—
484	D₄	—	8	1	no	—
485	D₄	—	8	2	no	—
486	D₄	—	8	2	no	—
487	D₄	—	8	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	4	4	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	8	2	no	—
499	C₂×C₄	—	8	1	no	—
500	C₂×C₄	—	8	2	no	—
501	C₂×C₄	C₁₉×#120	1	2	yes	—
502	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
503	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
504	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
505	C₈	—	2	4	no	—
506	C₈	—	4	4	no	—
507	C₂²	—	2	1	no	—
508	C₂²	—	2	2	no	—
509	C₂²	—	4	1	no	—
510	C₂²	—	4	2	no	—
511	C₂²	—	4	1	no	—
512	C₂²	—	4	2	no	—
513	C₂²	—	4	2	no	—
514	C₂²	—	4	2	no	—
515	C₂²	—	4	2	no	—
516	C₂²	—	8	4	no	—
517	C₂²	—	8	2	no	—
518	C₂²	—	8	4	no	—
519	C₂²	—	16	4	no	—
520	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
521	C₄	—	2	1	no	—
522	C₄	—	2	2	no	—
523	C₄	—	2	2	no	—
524	C₄	—	4	1	no	—
525	C₄	—	4	2	no	—
526	C₄	—	4	1	no	—
527	C₄	—	4	2	no	—
528	C₄	—	4	2	no	—
529	C₄	C₁₉×#453	1	2	yes	—
530	C₂	—	4	1	no	—
531	C₂	—	8	1	no	—
532	C₂	—	8	2	no	—
533	C₂	—	8	1	no	—
534	C₂	—	16	2	no	—
535	C₂	C₂×C₁₉×#453	1	1	yes	characteristic
536	C₂	C₁₉×#3021	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
LCS	G ▷ C₄² ▷ C₂² ▷ 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
1. C₁₉×#3529	C₂	semidirect
2. C₁₉×#3217	C₂	semidirect
3. C₁₉×#3151	C₂	semidirect
4. C₁₉×#1657	C₂	semidirect
5. C₁₉×#1656	C₂	semidirect
6. C₁₉×#1655	C₂	semidirect
7. C₁₉×#1536	C₂	semidirect
8. C₁₉×#1529	C₂	semidirect
12. C₁₉×#563	C₂²	semidirect
14. C₁₉×#562	C₂²	semidirect
15. C₁₉×H(3,𝔽₄)	C₂²	semidirect
20. C₂×C₁₉×#127	C₂²	semidirect
27. C₁₉×#496	C₂²	semidirect
30. C₁₉×#490	C₂²	semidirect
35. C₁₉×#432	C₂²	semidirect
36. C₄×M₁₆×C₁₉	C₂²	semidirect
37. C₁₉×#330	C₂²	semidirect
38. C₁₉×#329	C₂²	semidirect
39. C₁₉×#329	C₂²	semidirect
40. C₁₉×#329	C₂²	semidirect
189. #18995	C₁₉	direct (N × H)
239. #3529	C₂×C₁₉	semidirect
240. #3217	C₂×C₁₉	semidirect
241. #3151	C₂×C₁₉	semidirect
242. #1657	C₂×C₁₉	semidirect
243. #1656	C₂×C₁₉	semidirect
244. #1655	C₂×C₁₉	semidirect
245. #1536	C₂×C₁₉	semidirect
246. #1529	C₂×C₁₉	semidirect
273. #563	C₂²×C₁₉	semidirect
275. #562	C₂²×C₁₉	semidirect
276. H(3,𝔽₄)	C₂²×C₁₉	semidirect
281. C₂×#127	C₂²×C₁₉	semidirect
288. #496	C₂²×C₁₉	semidirect
291. #490	C₂²×C₁₉	semidirect
296. #432	C₂²×C₁₉	semidirect
297. C₄×M₁₆	C₂²×C₁₉	semidirect
298. #330	C₂²×C₁₉	semidirect
299. #329	C₂²×C₁₉	semidirect
300. #329	C₂²×C₁₉	semidirect
301. #329	C₂²×C₁₉	semidirect
383. C₁₉	#18995	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×#3529	2
C₁₉×#3217	2
C₁₉×#3151	2
C₁₉×#1657	2
C₁₉×#1656	2
C₁₉×#1655	2
C₁₉×#1536	2
C₁₉×#1529	2
#18995	19

Subgroups — C19×#18995 #18024954

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18995 #18024954