Subgroups — C₁₉×#12749 #18018708

Order 4864.

882 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#578	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#362	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#359	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2139	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#358	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₉×#350	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1816	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×2₋¹⁺⁴	—	2	1	no	—
9	C₁₉×#578	—	2	2	no	—
10	C₁₉×#578	—	2	2	no	—
11	C₁₉×#578	—	2	2	no	—
12	C₁₉×#578	C₄	1	4	yes	complemented
13	C₂×C₁₉×#137	—	2	2	no	—
14	C₂×C₁₉×#137	—	2	1	no	—
15	C₂×C₁₉×#135	—	2	1	no	—
16	C₂×C₁₉×#135	C₂²	1	1	yes	characteristic
17	C₂²×Q₁₆×C₁₉	—	2	1	no	—
18	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×M₃₂	C₂²	1	1	yes	characteristic
21	C₂²×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
24	C₁₉×#417	—	2	1	no	—
25	C₁₉×#362	—	2	2	no	—
26	C₁₉×#359	—	2	2	no	—
27	C₁₉×#358	—	2	2	no	—
28	C₁₉×#358	—	2	1	no	—
29	C₁₉×#357	—	2	1	no	—
30	C₁₉×#350	—	2	2	no	—
31	C₁₉×#343	—	2	1	no	—
32	C₁₉×2₋¹⁺⁴	—	2	4	no	—
33	C₁₉×2₋¹⁺⁴	—	2	4	no	—
34	C₁₉×2₋¹⁺⁴	—	4	2	no	—
35	C₁₉×2₋¹⁺⁴	—	4	2	no	—
36	C₂×#41×C₁₉	—	2	2	no	—
37	C₂×#41×C₁₉	—	2	1	no	—
38	C₂×#41×C₁₉	—	4	2	no	—
39	C₂×#41×C₁₉	—	4	1	no	—
40	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
41	C₂²×Q₈×C₁₉	—	2	2	no	—
42	C₂²×Q₈×C₁₉	—	2	1	no	—
43	C₂²×Q₈×C₁₉	—	4	1	no	—
44	C₁₉×#137	—	2	4	no	—
45	C₁₉×#137	—	2	8	no	—
46	C₁₉×#137	—	2	8	no	—
47	C₁₉×#137	—	2	4	no	—
48	C₁₉×#135	—	2	4	no	—
49	C₁₉×#135	—	2	4	no	—
50	C₁₉×#135	—	2	1	no	—
51	C₁₉×#135	—	2	1	no	—
52	C₁₉×#135	C₂×C₄	1	2	yes	—
53	C₁₉×#135	D₄	1	2	yes	—
54	C₂×Q₁₆×C₁₉	—	2	2	no	—
55	C₂×Q₁₆×C₁₉	—	2	4	no	—
56	C₂×Q₁₆×C₁₉	—	2	4	no	—
57	C₂×Q₁₆×C₁₉	—	2	1	no	—
58	C₂×Q₁₆×C₁₉	—	2	1	no	—
59	C₂×Q₁₆×C₁₉	—	2	1	no	—
60	C₂×Q₁₆×C₁₉	C₂×C₄	1	2	yes	—
61	C₂×Q₁₆×C₁₉	D₄	1	1	yes	characteristic
62	C₂×Q₁₆×C₁₉	D₄	1	2	yes	—
63	C₂×Q₁₆×C₁₉	D₄	1	2	yes	—
64	C₂×SD₁₆×C₁₉	—	2	2	no	—
65	C₂×SD₁₆×C₁₉	—	2	1	no	—
66	C₂×D₈×C₁₉	D₄	1	1	yes	characteristic
67	C₁₉×#131	—	2	1	no	—
68	C₁₉×#131	—	2	1	no	—
69	C₁₉×#131	C₂×C₄	1	2	yes	—
70	C₁₉×#131	D₄	1	2	yes	—
71	C₂×M₁₆×C₁₉	—	2	1	no	—
72	C₂×M₁₆×C₁₉	—	2	1	no	—
73	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
74	C₂²×C₈×C₁₉	—	2	1	no	—
75	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
77	C₁₉×M₃₂	—	2	1	no	—
78	C₁₉×M₃₂	—	2	1	no	—
79	C₂×C₁₆×C₁₉	—	2	1	no	—
80	C₂×C₁₆×C₁₉	—	2	1	no	—
81	C₂×C₁₆×C₁₉	—	2	1	no	—
82	C₂×C₁₆×C₁₉	—	2	1	no	—
83	C₁₉×#108	—	2	1	no	—
84	C₁₉×#108	—	2	1	no	—
85	C₁₉×#107	—	2	1	no	—
86	C₁₉×#107	—	2	1	no	—
87	C₁₉×#103	—	4	1	no	—
88	C₁₉×#102	—	4	1	no	—
89	#41×C₁₉	—	2	1	no	—
90	#41×C₁₉	—	2	1	no	—
91	#41×C₁₉	—	2	8	no	—
92	#41×C₁₉	—	2	2	no	—
93	#41×C₁₉	—	2	2	no	—
94	#41×C₁₉	—	4	4	no	—
95	#41×C₁₉	—	4	8	no	—
96	#41×C₁₉	—	4	8	no	—
97	#41×C₁₉	—	4	4	no	—
98	#41×C₁₉	—	4	4	no	—
99	#41×C₁₉	—	4	1	no	—
100	#41×C₁₉	—	4	1	no	—
101	#41×C₁₉	C₂²⋊C₄	1	2	yes	—
102	#41×C₁₉	SD₁₆	1	2	yes	—
103	C₂×Q₈×C₁₉	—	2	8	no	—
104	C₂×Q₈×C₁₉	—	2	2	no	—
105	C₂×Q₈×C₁₉	—	2	2	no	—
106	C₂×Q₈×C₁₉	—	2	1	no	—
107	C₂×Q₈×C₁₉	—	2	2	no	—
108	C₂×Q₈×C₁₉	—	4	2	no	—
109	C₂×Q₈×C₁₉	—	4	4	no	—
110	C₂×Q₈×C₁₉	—	4	4	no	—
111	C₂×Q₈×C₁₉	—	4	4	no	—
112	C₂×Q₈×C₁₉	—	4	1	no	—
113	C₂×Q₈×C₁₉	—	4	1	no	—
114	C₂×Q₈×C₁₉	—	4	1	no	—
115	C₂×Q₈×C₁₉	D₈	1	1	yes	characteristic
116	C₂×D₄×C₁₉	—	2	1	no	—
117	C₂×D₄×C₁₉	—	2	1	no	—
118	C₂×D₄×C₁₉	—	4	2	no	—
119	C₂×D₄×C₁₉	—	4	1	no	—
120	C₂×D₄×C₁₉	D₈	1	1	yes	characteristic
121	C₂²×C₄×C₁₉	—	2	1	no	—
122	C₂²×C₄×C₁₉	—	4	2	no	—
123	C₂²×C₄×C₁₉	—	4	2	no	—
124	C₂²×C₄×C₁₉	—	4	1	no	—
125	C₂²×C₄×C₁₉	—	4	1	no	—
126	C₂²×C₄×C₁₉	—	4	1	no	—
127	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
128	Q₁₆×C₁₉	—	2	8	no	—
129	Q₁₆×C₁₉	—	2	2	no	—
130	Q₁₆×C₁₉	—	2	1	no	—
131	Q₁₆×C₁₉	—	2	2	no	—
132	Q₁₆×C₁₉	—	2	2	no	—
133	Q₁₆×C₁₉	C₂²⋊C₄	1	2	yes	—
134	Q₁₆×C₁₉	C₂²⋊C₄	1	4	yes	—
135	SD₁₆×C₁₉	—	2	8	no	—
136	SD₁₆×C₁₉	—	2	2	no	—
137	SD₁₆×C₁₉	—	2	2	no	—
138	D₈×C₁₉	—	2	1	no	—
139	D₈×C₁₉	C₂²⋊C₄	1	2	yes	—
140	M₁₆×C₁₉	—	2	1	no	—
141	M₁₆×C₁₉	—	2	2	no	—
142	M₁₆×C₁₉	—	2	2	no	—
143	M₁₆×C₁₉	—	4	1	no	—
144	M₁₆×C₁₉	—	4	1	no	—
145	M₁₆×C₁₉	C₂²⋊C₄	1	2	yes	—
146	C₂×C₈×C₁₉	—	2	1	no	—
147	C₂×C₈×C₁₉	—	2	2	no	—
148	C₂×C₈×C₁₉	—	2	2	no	—
149	C₂×C₈×C₁₉	—	4	1	no	—
150	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
155	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
156	C₄⋊C₄×C₁₉	—	4	1	no	—
157	C₄⋊C₄×C₁₉	—	4	1	no	—
158	C₁₆×C₁₉	—	4	1	no	—
159	C₁₆×C₁₉	—	4	1	no	—
160	#12749	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
161	C₂³×C₁₉	—	2	1	no	—
162	C₂³×C₁₉	—	4	1	no	—
163	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
164	Q₈×C₁₉	—	2	1	no	—
165	Q₈×C₁₉	—	2	4	no	—
166	Q₈×C₁₉	—	2	2	no	—
167	Q₈×C₁₉	—	4	8	no	—
168	Q₈×C₁₉	—	4	2	no	—
169	Q₈×C₁₉	—	4	2	no	—
170	Q₈×C₁₉	—	4	1	no	—
171	Q₈×C₁₉	—	4	2	no	—
172	Q₈×C₁₉	#102	1	2	yes	—
173	D₄×C₁₉	—	2	2	no	—
174	D₄×C₁₉	—	2	2	no	—
175	D₄×C₁₉	—	2	2	no	—
176	D₄×C₁₉	—	2	1	no	—
177	D₄×C₁₉	—	4	8	no	—
178	D₄×C₁₉	—	4	2	no	—
179	D₄×C₁₉	—	4	2	no	—
180	D₄×C₁₉	—	4	1	no	—
181	D₄×C₁₉	#102	1	2	yes	—
182	C₂×C₄×C₁₉	—	2	1	no	—
183	C₂×C₄×C₁₉	—	2	2	no	—
184	C₂×C₄×C₁₉	—	2	2	no	—
185	C₂×C₄×C₁₉	—	4	8	no	—
186	C₂×C₄×C₁₉	—	4	8	no	—
187	C₂×C₄×C₁₉	—	4	2	no	—
188	C₂×C₄×C₁₉	—	4	2	no	—
189	C₂×C₄×C₁₉	—	4	1	no	—
190	C₂×C₄×C₁₉	—	4	2	no	—
191	C₂×C₄×C₁₉	—	4	2	no	—
192	C₂×C₄×C₁₉	—	4	2	no	—
193	C₂×C₄×C₁₉	—	8	1	no	—
194	C₂×C₄×C₁₉	—	16	1	no	—
195	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
196	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
197	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
198	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
199	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
200	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
201	C₈×C₁₉	—	2	2	no	—
202	C₈×C₁₉	—	8	1	no	—
203	C₈×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
204	C₈×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
205	C₈×C₁₉	#120	1	1	yes	characteristic
206	C₈×C₁₉	#120	1	1	yes	characteristic
207	C₂×#578	C₂×C₁₉	1	1	yes	characteristic
208	C₂×#362	C₂×C₁₉	1	1	yes	characteristic, complemented
209	C₂×#359	C₂×C₁₉	1	1	yes	characteristic, complemented
210	#2139	C₂×C₁₉	1	1	yes	characteristic, complemented
211	C₂×#358	C₂×C₁₉	1	1	yes	characteristic, complemented
212	C₂×#350	C₂×C₁₉	1	1	yes	characteristic, complemented
213	#1816	C₂×C₁₉	1	1	yes	characteristic, complemented
214	C₂²×C₁₉	—	2	1	no	—
215	C₂²×C₁₉	—	2	1	no	—
216	C₂²×C₁₉	—	2	2	no	—
217	C₂²×C₁₉	—	4	1	no	—
218	C₂²×C₁₉	—	4	1	no	—
219	C₂²×C₁₉	—	4	2	no	—
220	C₂²×C₁₉	—	8	1	no	—
221	C₂²×C₁₉	—	8	1	no	—
222	C₂²×C₁₉	#418	1	1	yes	characteristic
223	C₂²×C₁₉	#447	1	1	yes	characteristic
224	C₂²×C₁₉	#450	1	1	yes	characteristic
225	C₄×C₁₉	—	2	2	no	—
226	C₄×C₁₉	—	4	4	no	—
227	C₄×C₁₉	—	4	2	no	—
228	C₄×C₁₉	—	16	1	no	—
229	C₄×C₁₉	#379	1	1	yes	characteristic
230	C₄×C₁₉	C₂×#102	1	1	yes	characteristic
231	C₄×C₁₉	#447	1	1	yes	characteristic
232	C₄×C₁₉	#450	1	1	yes	characteristic
233	C₂×2₋¹⁺⁴	—	2	1	no	—
234	#578	—	2	2	no	—
235	#578	—	2	2	no	—
236	#578	—	2	2	no	—
237	#578	C₄×C₁₉	1	4	yes	complemented
238	C₂×#137	—	2	2	no	—
239	C₂×#137	—	2	1	no	—
240	C₂×#135	—	2	1	no	—
241	C₂×#135	C₂²×C₁₉	1	1	yes	characteristic
242	C₂²×Q₁₆	—	2	1	no	—
243	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
244	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic
245	C₂×M₃₂	C₂²×C₁₉	1	1	yes	characteristic
246	C₂²×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
247	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
248	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
249	#417	—	2	1	no	—
250	#362	—	2	2	no	—
251	#359	—	2	2	no	—
252	#358	—	2	2	no	—
253	#358	—	2	1	no	—
254	#357	—	2	1	no	—
255	#350	—	2	2	no	—
256	#343	—	2	1	no	—
257	C₂×C₁₉	—	2	1	no	—
258	C₂×C₁₉	—	2	1	no	—
259	C₂×C₁₉	—	4	2	no	—
260	C₂×C₁₉	—	8	2	no	—
261	C₂×C₁₉	#1786	1	1	yes	characteristic
262	C₂×C₁₉	#2193	1	1	yes	characteristic
263	C₂×C₁₉	#2195	1	1	yes	characteristic
264	2₋¹⁺⁴	—	2	4	no	—
265	2₋¹⁺⁴	—	2	4	no	—
266	2₋¹⁺⁴	—	4	2	no	—
267	2₋¹⁺⁴	—	4	2	no	—
268	C₂×#41	—	2	2	no	—
269	C₂×#41	—	2	1	no	—
270	C₂×#41	—	4	2	no	—
271	C₂×#41	—	4	1	no	—
272	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
273	C₂²×Q₈	—	2	2	no	—
274	C₂²×Q₈	—	2	1	no	—
275	C₂²×Q₈	—	4	1	no	—
276	#137	—	2	4	no	—
277	#137	—	2	8	no	—
278	#137	—	2	8	no	—
279	#137	—	2	4	no	—
280	#135	—	2	4	no	—
281	#135	—	2	4	no	—
282	#135	—	2	1	no	—
283	#135	—	2	1	no	—
284	#135	C₂×C₄×C₁₉	1	2	yes	—
285	#135	D₄×C₁₉	1	2	yes	—
286	C₂×Q₁₆	—	2	2	no	—
287	C₂×Q₁₆	—	2	4	no	—
288	C₂×Q₁₆	—	2	4	no	—
289	C₂×Q₁₆	—	2	1	no	—
290	C₂×Q₁₆	—	2	1	no	—
291	C₂×Q₁₆	—	2	1	no	—
292	C₂×Q₁₆	C₂×C₄×C₁₉	1	2	yes	—
293	C₂×Q₁₆	D₄×C₁₉	1	1	yes	characteristic
294	C₂×Q₁₆	D₄×C₁₉	1	2	yes	—
295	C₂×Q₁₆	D₄×C₁₉	1	2	yes	—
296	C₂×SD₁₆	—	2	2	no	—
297	C₂×SD₁₆	—	2	1	no	—
298	C₂×D₈	D₄×C₁₉	1	1	yes	characteristic
299	#131	—	2	1	no	—
300	#131	—	2	1	no	—
301	#131	C₂×C₄×C₁₉	1	2	yes	—
302	#131	D₄×C₁₉	1	2	yes	—
303	C₂×M₁₆	—	2	1	no	—
304	C₂×M₁₆	—	2	1	no	—
305	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
306	C₂²×C₈	—	2	1	no	—
307	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
308	C₂×C₄⋊C₄	—	2	1	no	—
309	M₃₂	—	2	1	no	—
310	M₃₂	—	2	1	no	—
311	C₂×C₁₆	—	2	1	no	—
312	C₂×C₁₆	—	2	1	no	—
313	C₂×C₁₆	—	2	1	no	—
314	C₂×C₁₆	—	2	1	no	—
315	#108	—	2	1	no	—
316	#108	—	2	1	no	—
317	#107	—	2	1	no	—
318	#107	—	2	1	no	—
319	#103	—	4	1	no	—
320	#102	—	4	1	no	—
321	C₁₉	#12749	1	1	yes	characteristic, direct product factor, Sylow
322	#41	—	2	1	no	—
323	#41	—	2	1	no	—
324	#41	—	2	8	no	—
325	#41	—	2	2	no	—
326	#41	—	2	2	no	—
327	#41	—	4	4	no	—
328	#41	—	4	8	no	—
329	#41	—	4	8	no	—
330	#41	—	4	4	no	—
331	#41	—	4	4	no	—
332	#41	—	4	1	no	—
333	#41	—	4	1	no	—
334	#41	C₂²⋊C₄×C₁₉	1	2	yes	—
335	#41	SD₁₆×C₁₉	1	2	yes	—
336	C₂×Q₈	—	2	8	no	—
337	C₂×Q₈	—	2	2	no	—
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	4	2	no	—
342	C₂×Q₈	—	4	4	no	—
343	C₂×Q₈	—	4	4	no	—
344	C₂×Q₈	—	4	4	no	—
345	C₂×Q₈	—	4	1	no	—
346	C₂×Q₈	—	4	1	no	—
347	C₂×Q₈	—	4	1	no	—
348	C₂×Q₈	D₈×C₁₉	1	1	yes	characteristic
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	—	2	1	no	—
351	C₂×D₄	—	4	2	no	—
352	C₂×D₄	—	4	1	no	—
353	C₂×D₄	D₈×C₁₉	1	1	yes	characteristic
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	4	2	no	—
356	C₂²×C₄	—	4	2	no	—
357	C₂²×C₄	—	4	1	no	—
358	C₂²×C₄	—	4	1	no	—
359	C₂²×C₄	—	4	1	no	—
360	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
361	Q₁₆	—	2	8	no	—
362	Q₁₆	—	2	2	no	—
363	Q₁₆	—	2	1	no	—
364	Q₁₆	—	2	2	no	—
365	Q₁₆	—	2	2	no	—
366	Q₁₆	C₂²⋊C₄×C₁₉	1	2	yes	—
367	Q₁₆	C₂²⋊C₄×C₁₉	1	4	yes	—
368	SD₁₆	—	2	8	no	—
369	SD₁₆	—	2	2	no	—
370	SD₁₆	—	2	2	no	—
371	D₈	—	2	1	no	—
372	D₈	C₂²⋊C₄×C₁₉	1	2	yes	—
373	M₁₆	—	2	1	no	—
374	M₁₆	—	2	2	no	—
375	M₁₆	—	2	2	no	—
376	M₁₆	—	4	1	no	—
377	M₁₆	—	4	1	no	—
378	M₁₆	C₂²⋊C₄×C₁₉	1	2	yes	—
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	4	1	no	—
383	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
384	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
385	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
386	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
387	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
388	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
389	C₄⋊C₄	—	4	1	no	—
390	C₄⋊C₄	—	4	1	no	—
391	C₁₆	—	4	1	no	—
392	C₁₆	—	4	1	no	—
393	C₂³	—	2	1	no	—
394	C₂³	—	4	1	no	—
395	C₂³	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
396	Q₈	—	2	1	no	—
397	Q₈	—	2	4	no	—
398	Q₈	—	2	2	no	—
399	Q₈	—	4	8	no	—
400	Q₈	—	4	2	no	—
401	Q₈	—	4	2	no	—
402	Q₈	—	4	1	no	—
403	Q₈	—	4	2	no	—
404	Q₈	C₁₉×#102	1	2	yes	—
405	D₄	—	2	2	no	—
406	D₄	—	2	2	no	—
407	D₄	—	2	2	no	—
408	D₄	—	2	1	no	—
409	D₄	—	4	8	no	—
410	D₄	—	4	2	no	—
411	D₄	—	4	2	no	—
412	D₄	—	4	1	no	—
413	D₄	C₁₉×#102	1	2	yes	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	4	8	no	—
418	C₂×C₄	—	4	8	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	8	1	no	—
426	C₂×C₄	—	16	1	no	—
427	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
428	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
429	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
430	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
431	C₂×C₄	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
432	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
433	C₈	—	2	2	no	—
434	C₈	—	8	1	no	—
435	C₈	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
436	C₈	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
437	C₈	C₁₉×#120	1	1	yes	characteristic
438	C₈	C₁₉×#120	1	1	yes	characteristic
439	C₂²	—	2	1	no	—
440	C₂²	—	2	1	no	—
441	C₂²	—	2	2	no	—
442	C₂²	—	4	1	no	—
443	C₂²	—	4	1	no	—
444	C₂²	—	4	2	no	—
445	C₂²	—	8	1	no	—
446	C₂²	—	8	1	no	—
447	C₂²	C₁₉×#418	1	1	yes	characteristic
448	C₂²	C₁₉×#447	1	1	yes	characteristic
449	C₂²	C₁₉×#450	1	1	yes	characteristic
450	C₄	—	2	2	no	—
451	C₄	—	4	4	no	—
452	C₄	—	4	2	no	—
453	C₄	—	16	1	no	—
454	C₄	C₁₉×#379	1	1	yes	characteristic
455	C₄	C₂×C₁₉×#102	1	1	yes	characteristic
456	C₄	C₁₉×#447	1	1	yes	characteristic
457	C₄	C₁₉×#450	1	1	yes	characteristic
458	C₂	—	2	1	no	—
459	C₂	—	2	1	no	—
460	C₂	—	4	2	no	—
461	C₂	—	8	2	no	—
462	C₂	C₁₉×#1786	1	1	yes	characteristic
463	C₂	C₁₉×#2193	1	1	yes	characteristic
464	C₂	C₁₉×#2195	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#447
commutator	C₂×C₈	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
prime radical	C₂×C₁₉×#578	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₁₉×#131 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#362	C₂	semidirect
3. C₂×C₁₉×#359	C₂	semidirect
4. C₁₉×#2139	C₂	semidirect
5. C₂×C₁₉×#358	C₂	semidirect
6. C₂×C₁₉×#350	C₂	semidirect
7. C₁₉×#1816	C₂	semidirect
12. C₁₉×#578	C₄	semidirect
160. #12749	C₁₉	direct (N × H)
208. C₂×#362	C₂×C₁₉	semidirect
209. C₂×#359	C₂×C₁₉	semidirect
210. #2139	C₂×C₁₉	semidirect
211. C₂×#358	C₂×C₁₉	semidirect
212. C₂×#350	C₂×C₁₉	semidirect
213. #1816	C₂×C₁₉	semidirect
237. #578	C₄×C₁₉	semidirect
321. C₁₉	#12749	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#578	2
C₂×C₁₉×#362	2
C₂×C₁₉×#359	2
C₁₉×#2139	2
C₂×C₁₉×#358	2
C₂×C₁₉×#350	2
C₁₉×#1816	2
#12749	19

Subgroups — C19×#12749 #18018708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#12749 #18018708