Subgroups — C₁₉×#32942 #18038901

Order 4864.

1368 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#131	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#472	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#466	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3006	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1907	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1900	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1816	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1810	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	4	yes	—
11	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
12	C₂×C₁₉×#131	—	2	8	no	—
13	C₂×C₁₉×#131	—	2	1	no	—
14	C₂×C₁₉×#131	—	2	1	no	—
15	C₂×C₁₉×#131	C₂²	1	2	yes	—
16	C₂×C₁₉×#131	C₂²	1	2	yes	—
17	C₂²×M₁₆×C₁₉	—	2	1	no	—
18	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₁₉	—	2	1	no	—
20	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#121	C₂²	1	2	yes	—
22	C₁₉×#472	—	2	8	no	—
23	C₁₉×#466	—	2	1	no	—
24	C₁₉×#466	—	2	1	no	—
25	C₁₉×#466	—	2	1	no	—
26	C₁₉×#466	—	2	1	no	—
27	C₁₉×#449	—	2	4	no	—
28	C₁₉×#448	—	2	2	no	—
29	C₁₉×#447	—	2	2	no	—
30	C₂×C₁₉×#108	C₂²	1	2	yes	complemented
31	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic, complemented
32	C₁₉×#417	C₂²	1	4	yes	—
33	C₂×C₁₉×#102	C₂²	1	2	yes	complemented
34	C₂×C₁₉×#100	C₂²	1	4	yes	complemented
35	C₁₉×#407	C₂²	1	2	yes	—
36	C₁₉×#343	C₂²	1	4	yes	complemented
37	C₁₉×#341	C₂²	1	2	yes	complemented
38	C₂×#41×C₁₉	—	2	4	no	—
39	C₂×#41×C₁₉	—	2	4	no	—
40	C₂×#41×C₁₉	—	2	1	no	—
41	C₂×#41×C₁₉	—	2	1	no	—
42	C₂×#41×C₁₉	D₄	1	2	yes	—
43	C₂×#41×C₁₉	C₂³	1	2	yes	—
44	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
45	C₂²×D₄×C₁₉	—	2	1	no	—
46	C₂²×D₄×C₁₉	—	2	2	no	—
47	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
48	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
49	C₂³×C₄×C₁₉	—	2	1	no	—
50	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
51	C₁₉×AGL(1,ℤ/8)	—	2	8	no	—
52	C₁₉×AGL(1,ℤ/8)	—	2	8	no	—
53	C₂×SD₁₆×C₁₉	—	2	4	no	—
54	C₂×D₈×C₁₉	—	2	4	no	—
55	C₂×D₈×C₁₉	—	2	1	no	—
56	C₂×D₈×C₁₉	—	2	1	no	—
57	C₂×D₈×C₁₉	—	2	4	no	—
58	C₁₉×#131	—	2	8	no	—
59	C₁₉×#131	—	2	8	no	—
60	C₁₉×#131	—	2	4	no	—
61	C₁₉×#131	—	2	4	no	—
62	C₁₉×#131	—	2	4	no	—
63	C₁₉×#131	D₄	1	8	yes	complemented
64	C₂×M₁₆×C₁₉	—	2	8	no	—
65	C₂×M₁₆×C₁₉	—	2	1	no	—
66	C₂×M₁₆×C₁₉	—	2	4	no	—
67	C₂×M₁₆×C₁₉	—	2	2	no	—
68	C₂×M₁₆×C₁₉	—	2	2	no	—
69	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
70	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
71	C₂²×C₈×C₁₉	—	2	8	no	—
72	C₂²×C₈×C₁₉	—	2	1	no	—
73	C₂²×C₈×C₁₉	—	2	2	no	—
74	C₂²×C₈×C₁₉	—	2	2	no	—
75	C₂²×C₈×C₁₉	—	2	4	no	—
76	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
77	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
78	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
79	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
80	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
82	C₁₉×#121	—	2	2	no	—
83	C₁₉×#121	—	2	2	no	—
84	C₁₉×#121	—	2	2	no	—
85	C₁₉×#121	—	2	2	no	—
86	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
87	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
88	C₁₉×#108	—	2	4	no	—
89	C₁₉×#107	—	2	1	no	—
90	C₁₉×#107	—	2	1	no	—
91	C₁₉×#103	—	2	4	no	—
92	C₁₉×#102	—	2	4	no	—
93	C₁₉×#102	—	2	2	no	—
94	C₁₉×#102	—	2	2	no	—
95	C₁₉×#100	—	2	8	no	—
96	C₁₉×C₂²⋊C₈	—	2	2	no	—
97	C₁₉×C₂²⋊C₈	—	2	2	no	—
98	C₂⁴×C₁₉	—	2	1	no	—
99	C₂⁴×C₁₉	—	2	2	no	—
100	C₂⁴×C₁₉	#41	1	1	yes	characteristic
101	#41×C₁₉	—	2	4	no	—
102	#41×C₁₉	—	2	8	no	—
103	#41×C₁₉	—	2	4	no	—
104	#41×C₁₉	—	2	4	no	—
105	#41×C₁₉	—	2	4	no	—
106	#41×C₁₉	—	2	2	no	—
107	#41×C₁₉	—	2	2	no	—
108	#41×C₁₉	C₂×D₄	1	4	yes	—
109	#41×C₁₉	#41	1	4	yes	—
110	C₂×Q₈×C₁₉	—	2	4	no	—
111	C₂×Q₈×C₁₉	—	2	1	no	—
112	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
113	C₂×D₄×C₁₉	—	2	8	no	—
114	C₂×D₄×C₁₉	—	2	2	no	—
115	C₂×D₄×C₁₉	—	2	2	no	—
116	C₂×D₄×C₁₉	—	2	4	no	—
117	C₂×D₄×C₁₉	—	2	1	no	—
118	C₂×D₄×C₁₉	—	2	2	no	—
119	C₂×D₄×C₁₉	—	2	2	no	—
120	C₂×D₄×C₁₉	—	2	4	no	—
121	C₂×D₄×C₁₉	—	2	4	no	—
122	C₂×D₄×C₁₉	—	4	2	no	—
123	C₂×D₄×C₁₉	—	4	2	no	—
124	C₂×D₄×C₁₉	—	8	4	no	—
125	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₁₉	—	2	4	no	—
127	C₂²×C₄×C₁₉	—	2	4	no	—
128	C₂²×C₄×C₁₉	—	2	1	no	—
129	C₂²×C₄×C₁₉	—	2	2	no	—
130	C₂²×C₄×C₁₉	—	2	2	no	—
131	C₂²×C₄×C₁₉	—	2	2	no	—
132	C₂²×C₄×C₁₉	—	2	2	no	—
133	C₂²×C₄×C₁₉	—	2	2	no	—
134	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
139	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
140	SD₁₆×C₁₉	—	4	8	no	—
141	D₈×C₁₉	—	4	8	no	—
142	D₈×C₁₉	—	4	2	no	—
143	D₈×C₁₉	—	4	2	no	—
144	M₁₆×C₁₉	—	2	4	no	—
145	M₁₆×C₁₉	—	2	8	no	—
146	M₁₆×C₁₉	—	2	2	no	—
147	M₁₆×C₁₉	—	2	8	no	—
148	M₁₆×C₁₉	—	2	4	no	—
149	M₁₆×C₁₉	—	2	4	no	—
150	M₁₆×C₁₉	C₂×D₄	1	4	yes	—
151	C₂×C₈×C₁₉	—	2	4	no	—
152	C₂×C₈×C₁₉	—	2	8	no	—
153	C₂×C₈×C₁₉	—	2	2	no	—
154	C₂×C₈×C₁₉	—	2	2	no	—
155	C₂×C₈×C₁₉	—	2	2	no	—
156	C₂×C₈×C₁₉	—	2	8	no	—
157	C₂×C₈×C₁₉	—	2	2	no	—
158	C₂×C₈×C₁₉	—	2	2	no	—
159	C₂×C₈×C₁₉	—	2	2	no	—
160	C₂×C₈×C₁₉	—	2	4	no	—
161	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
162	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
163	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
164	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
165	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
166	C₄⋊C₄×C₁₉	—	2	2	no	—
167	C₄⋊C₄×C₁₉	—	2	2	no	—
168	C₂²⋊C₄×C₁₉	—	4	2	no	—
169	C₂²⋊C₄×C₁₉	—	4	2	no	—
170	#32942	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
171	C₂³×C₁₉	—	2	4	no	—
172	C₂³×C₁₉	—	2	2	no	—
173	C₂³×C₁₉	—	2	2	no	—
174	C₂³×C₁₉	—	2	2	no	—
175	C₂³×C₁₉	—	4	1	no	—
176	C₂³×C₁₉	—	4	2	no	—
177	C₂³×C₁₉	—	4	2	no	—
178	C₂³×C₁₉	—	4	2	no	—
179	C₂³×C₁₉	—	4	4	no	—
180	C₂³×C₁₉	—	8	2	no	—
181	C₂³×C₁₉	—	8	2	no	—
182	C₂³×C₁₉	#121	1	1	yes	characteristic
183	C₂³×C₁₉	#121	1	1	yes	characteristic
184	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
185	Q₈×C₁₉	—	2	4	no	—
186	Q₈×C₁₉	—	2	2	no	—
187	Q₈×C₁₉	#121	1	4	yes	—
188	D₄×C₁₉	—	2	8	no	—
189	D₄×C₁₉	—	2	4	no	—
190	D₄×C₁₉	—	2	4	no	—
191	D₄×C₁₉	—	2	4	no	—
192	D₄×C₁₉	—	2	2	no	—
193	D₄×C₁₉	—	4	2	no	—
194	D₄×C₁₉	—	4	4	no	—
195	D₄×C₁₉	—	4	2	no	—
196	D₄×C₁₉	—	8	4	no	—
197	D₄×C₁₉	—	8	4	no	—
198	D₄×C₁₉	#121	1	4	yes	—
199	C₂×C₄×C₁₉	—	2	4	no	—
200	C₂×C₄×C₁₉	—	2	8	no	—
201	C₂×C₄×C₁₉	—	2	2	no	—
202	C₂×C₄×C₁₉	—	2	2	no	—
203	C₂×C₄×C₁₉	—	2	1	no	—
204	C₂×C₄×C₁₉	—	2	4	no	—
205	C₂×C₄×C₁₉	—	2	1	no	—
206	C₂×C₄×C₁₉	—	2	2	no	—
207	C₂×C₄×C₁₉	—	2	2	no	—
208	C₂×C₄×C₁₉	—	2	1	no	—
209	C₂×C₄×C₁₉	—	2	4	no	—
210	C₂×C₄×C₁₉	—	2	1	no	—
211	C₂×C₄×C₁₉	—	4	2	no	—
212	C₂×C₄×C₁₉	—	8	2	no	—
213	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
214	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
215	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
216	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
219	C₈×C₁₉	—	2	1	no	—
220	C₈×C₁₉	—	2	4	no	—
221	C₈×C₁₉	—	2	1	no	—
222	C₈×C₁₉	—	4	4	no	—
223	C₈×C₁₉	#120	1	2	yes	—
224	C₈×C₁₉	#120	1	2	yes	—
225	C₂²×#131	C₂×C₁₉	1	1	yes	characteristic, complemented
226	C₂×#472	C₂×C₁₉	1	2	yes	complemented
227	C₂×#466	C₂×C₁₉	1	1	yes	characteristic, complemented
228	#3006	C₂×C₁₉	1	2	yes	complemented
229	#1907	C₂×C₁₉	1	4	yes	complemented
230	#1900	C₂×C₁₉	1	2	yes	complemented
231	#1816	C₂×C₁₉	1	2	yes	complemented
232	#1810	C₂×C₁₉	1	1	yes	characteristic, complemented
233	C₂²×C₁₉	—	2	1	no	—
234	C₂²×C₁₉	—	2	1	no	—
235	C₂²×C₁₉	—	2	1	no	—
236	C₂²×C₁₉	—	2	1	no	—
237	C₂²×C₁₉	—	2	1	no	—
238	C₂²×C₁₉	—	2	4	no	—
239	C₂²×C₁₉	—	2	1	no	—
240	C₂²×C₁₉	—	2	1	no	—
241	C₂²×C₁₉	—	4	4	no	—
242	C₂²×C₁₉	—	4	8	no	—
243	C₂²×C₁₉	—	4	2	no	—
244	C₂²×C₁₉	—	4	2	no	—
245	C₂²×C₁₉	—	8	2	no	—
246	C₂²×C₁₉	—	8	2	no	—
247	C₂²×C₁₉	—	8	2	no	—
248	C₂²×C₁₉	—	16	4	no	—
249	C₂²×C₁₉	#472	1	2	yes	complemented
250	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
251	C₂²×C₁₉	#525	1	2	yes	—
252	C₄×C₁₉	—	2	1	no	—
253	C₄×C₁₉	—	2	4	no	—
254	C₄×C₁₉	—	2	1	no	—
255	C₄×C₁₉	—	8	2	no	—
256	C₄×C₁₉	C₂×#120	1	1	yes	characteristic
257	C₄×C₁₉	C₂×#121	1	2	yes	—
258	C₄×C₁₉	#525	1	1	yes	characteristic
259	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
260	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	4	yes	—
261	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
262	C₂×#131	—	2	8	no	—
263	C₂×#131	—	2	1	no	—
264	C₂×#131	—	2	1	no	—
265	C₂×#131	C₂²×C₁₉	1	2	yes	—
266	C₂×#131	C₂²×C₁₉	1	2	yes	—
267	C₂²×M₁₆	—	2	1	no	—
268	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
269	C₂³×C₈	—	2	1	no	—
270	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
271	C₂×#121	C₂²×C₁₉	1	2	yes	—
272	#472	—	2	8	no	—
273	#466	—	2	1	no	—
274	#466	—	2	1	no	—
275	#466	—	2	1	no	—
276	#466	—	2	1	no	—
277	#449	—	2	4	no	—
278	#448	—	2	2	no	—
279	#447	—	2	2	no	—
280	C₂×#108	C₂²×C₁₉	1	2	yes	complemented
281	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic, complemented
282	#417	C₂²×C₁₉	1	4	yes	—
283	C₂×#102	C₂²×C₁₉	1	2	yes	complemented
284	C₂×#100	C₂²×C₁₉	1	4	yes	complemented
285	#407	C₂²×C₁₉	1	2	yes	—
286	#343	C₂²×C₁₉	1	4	yes	complemented
287	#341	C₂²×C₁₉	1	2	yes	complemented
288	C₂×C₁₉	—	2	2	no	—
289	C₂×C₁₉	—	2	2	no	—
290	C₂×C₁₉	—	4	1	no	—
291	C₂×C₁₉	—	4	4	no	—
292	C₂×C₁₉	—	16	2	no	—
293	C₂×C₁₉	#2847	1	1	yes	characteristic
294	C₂×C₁₉	C₂×#472	1	1	yes	characteristic
295	C₂×C₁₉	#3067	1	1	yes	characteristic
296	C₂×#41	—	2	4	no	—
297	C₂×#41	—	2	4	no	—
298	C₂×#41	—	2	1	no	—
299	C₂×#41	—	2	1	no	—
300	C₂×#41	D₄×C₁₉	1	2	yes	—
301	C₂×#41	C₂³×C₁₉	1	2	yes	—
302	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
303	C₂²×D₄	—	2	1	no	—
304	C₂²×D₄	—	2	2	no	—
305	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
306	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
307	C₂³×C₄	—	2	1	no	—
308	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
309	AGL(1,ℤ/8)	—	2	8	no	—
310	AGL(1,ℤ/8)	—	2	8	no	—
311	C₂×SD₁₆	—	2	4	no	—
312	C₂×D₈	—	2	4	no	—
313	C₂×D₈	—	2	1	no	—
314	C₂×D₈	—	2	1	no	—
315	C₂×D₈	—	2	4	no	—
316	#131	—	2	8	no	—
317	#131	—	2	8	no	—
318	#131	—	2	4	no	—
319	#131	—	2	4	no	—
320	#131	—	2	4	no	—
321	#131	D₄×C₁₉	1	8	yes	complemented
322	C₂×M₁₆	—	2	8	no	—
323	C₂×M₁₆	—	2	1	no	—
324	C₂×M₁₆	—	2	4	no	—
325	C₂×M₁₆	—	2	2	no	—
326	C₂×M₁₆	—	2	2	no	—
327	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
328	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
329	C₂²×C₈	—	2	8	no	—
330	C₂²×C₈	—	2	1	no	—
331	C₂²×C₈	—	2	2	no	—
332	C₂²×C₈	—	2	2	no	—
333	C₂²×C₈	—	2	4	no	—
334	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
335	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
336	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
337	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
338	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
339	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
340	#121	—	2	2	no	—
341	#121	—	2	2	no	—
342	#121	—	2	2	no	—
343	#121	—	2	2	no	—
344	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
345	C₂×C₂²⋊C₄	—	2	2	no	—
346	#108	—	2	4	no	—
347	#107	—	2	1	no	—
348	#107	—	2	1	no	—
349	#103	—	2	4	no	—
350	#102	—	2	4	no	—
351	#102	—	2	2	no	—
352	#102	—	2	2	no	—
353	#100	—	2	8	no	—
354	C₂²⋊C₈	—	2	2	no	—
355	C₂²⋊C₈	—	2	2	no	—
356	C₁₉	#32942	1	1	yes	characteristic, direct product factor, Sylow
357	C₂⁴	—	2	1	no	—
358	C₂⁴	—	2	2	no	—
359	C₂⁴	#41×C₁₉	1	1	yes	characteristic
360	#41	—	2	4	no	—
361	#41	—	2	8	no	—
362	#41	—	2	4	no	—
363	#41	—	2	4	no	—
364	#41	—	2	4	no	—
365	#41	—	2	2	no	—
366	#41	—	2	2	no	—
367	#41	C₂×D₄×C₁₉	1	4	yes	—
368	#41	#41×C₁₉	1	4	yes	—
369	C₂×Q₈	—	2	4	no	—
370	C₂×Q₈	—	2	1	no	—
371	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
372	C₂×D₄	—	2	8	no	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	2	4	no	—
376	C₂×D₄	—	2	1	no	—
377	C₂×D₄	—	2	4	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	—	2	4	no	—
381	C₂×D₄	—	4	2	no	—
382	C₂×D₄	—	4	2	no	—
383	C₂×D₄	—	8	4	no	—
384	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
385	C₂²×C₄	—	2	4	no	—
386	C₂²×C₄	—	2	4	no	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
394	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
395	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
396	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
397	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
398	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
399	SD₁₆	—	4	8	no	—
400	D₈	—	4	8	no	—
401	D₈	—	4	2	no	—
402	D₈	—	4	2	no	—
403	M₁₆	—	2	4	no	—
404	M₁₆	—	2	8	no	—
405	M₁₆	—	2	2	no	—
406	M₁₆	—	2	8	no	—
407	M₁₆	—	2	4	no	—
408	M₁₆	—	2	4	no	—
409	M₁₆	C₂×D₄×C₁₉	1	4	yes	—
410	C₂×C₈	—	2	4	no	—
411	C₂×C₈	—	2	8	no	—
412	C₂×C₈	—	2	2	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	8	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	2	no	—
418	C₂×C₈	—	2	2	no	—
419	C₂×C₈	—	2	4	no	—
420	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
421	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
422	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
423	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
424	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	2	no	—
427	C₂²⋊C₄	—	4	2	no	—
428	C₂²⋊C₄	—	4	2	no	—
429	C₂³	—	2	4	no	—
430	C₂³	—	2	2	no	—
431	C₂³	—	2	2	no	—
432	C₂³	—	2	2	no	—
433	C₂³	—	4	1	no	—
434	C₂³	—	4	2	no	—
435	C₂³	—	4	2	no	—
436	C₂³	—	4	2	no	—
437	C₂³	—	4	4	no	—
438	C₂³	—	8	2	no	—
439	C₂³	—	8	2	no	—
440	C₂³	C₁₉×#121	1	1	yes	characteristic
441	C₂³	C₁₉×#121	1	1	yes	characteristic
442	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
443	Q₈	—	2	4	no	—
444	Q₈	—	2	2	no	—
445	Q₈	C₁₉×#121	1	4	yes	—
446	D₄	—	2	8	no	—
447	D₄	—	2	4	no	—
448	D₄	—	2	4	no	—
449	D₄	—	2	4	no	—
450	D₄	—	2	2	no	—
451	D₄	—	4	2	no	—
452	D₄	—	4	4	no	—
453	D₄	—	4	2	no	—
454	D₄	—	8	4	no	—
455	D₄	—	8	4	no	—
456	D₄	C₁₉×#121	1	4	yes	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	8	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	8	2	no	—
471	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
472	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
473	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
474	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
475	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
476	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
477	C₈	—	2	1	no	—
478	C₈	—	2	4	no	—
479	C₈	—	2	1	no	—
480	C₈	—	4	4	no	—
481	C₈	C₁₉×#120	1	2	yes	—
482	C₈	C₁₉×#120	1	2	yes	—
483	C₂²	—	2	1	no	—
484	C₂²	—	2	1	no	—
485	C₂²	—	2	1	no	—
486	C₂²	—	2	1	no	—
487	C₂²	—	2	1	no	—
488	C₂²	—	2	1	no	—
489	C₂²	—	2	1	no	—
490	C₂²	—	2	4	no	—
491	C₂²	—	4	4	no	—
492	C₂²	—	4	8	no	—
493	C₂²	—	4	2	no	—
494	C₂²	—	4	2	no	—
495	C₂²	—	8	2	no	—
496	C₂²	—	8	2	no	—
497	C₂²	—	8	2	no	—
498	C₂²	—	16	4	no	—
499	C₂²	C₁₉×#472	1	2	yes	complemented
500	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
501	C₂²	C₁₉×#525	1	2	yes	—
502	C₄	—	2	1	no	—
503	C₄	—	2	4	no	—
504	C₄	—	2	1	no	—
505	C₄	—	8	2	no	—
506	C₄	C₂×C₁₉×#120	1	1	yes	characteristic
507	C₄	C₂×C₁₉×#121	1	2	yes	—
508	C₄	C₁₉×#525	1	1	yes	characteristic
509	C₂	—	2	2	no	—
510	C₂	—	2	2	no	—
511	C₂	—	4	1	no	—
512	C₂	—	4	4	no	—
513	C₂	—	16	2	no	—
514	C₂	C₁₉×#2847	1	1	yes	characteristic
515	C₂	C₂×C₁₉×#472	1	1	yes	characteristic
516	C₂	C₁₉×#3067	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₉×#131	C₂	semidirect
2. C₂×C₁₉×#472	C₂	semidirect
3. C₂×C₁₉×#466	C₂	semidirect
4. C₁₉×#3006	C₂	semidirect
5. C₁₉×#1907	C₂	semidirect
6. C₁₉×#1900	C₂	semidirect
7. C₁₉×#1816	C₂	semidirect
8. C₁₉×#1810	C₂	semidirect
11. C₂²×D₈×C₁₉	C₂²	semidirect
30. C₂×C₁₉×#108	C₂²	semidirect
31. C₂×C₁₉×#107	C₂²	semidirect
33. C₂×C₁₉×#102	C₂²	semidirect
34. C₂×C₁₉×#100	C₂²	semidirect
36. C₁₉×#343	C₂²	semidirect
37. C₁₉×#341	C₂²	semidirect
63. C₁₉×#131	D₄	semidirect
170. #32942	C₁₉	direct (N × H)
225. C₂²×#131	C₂×C₁₉	semidirect
226. C₂×#472	C₂×C₁₉	semidirect
227. C₂×#466	C₂×C₁₉	semidirect
228. #3006	C₂×C₁₉	semidirect
229. #1907	C₂×C₁₉	semidirect
230. #1900	C₂×C₁₉	semidirect
231. #1816	C₂×C₁₉	semidirect
232. #1810	C₂×C₁₉	semidirect
249. C₂²×C₁₉	#472	semidirect
261. C₂²×D₈	C₂²×C₁₉	semidirect
280. C₂×#108	C₂²×C₁₉	semidirect
281. C₂×#107	C₂²×C₁₉	semidirect
283. C₂×#102	C₂²×C₁₉	semidirect
284. C₂×#100	C₂²×C₁₉	semidirect
286. #343	C₂²×C₁₉	semidirect
287. #341	C₂²×C₁₉	semidirect
321. #131	D₄×C₁₉	semidirect
356. C₁₉	#32942	direct (N × H)
499. C₂²	C₁₉×#472	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×#131	2
C₂×C₁₉×#472	2
C₂×C₁₉×#466	2
C₁₉×#3006	2
C₁₉×#1907	2
C₁₉×#1900	2
C₁₉×#1816	2
C₁₉×#1810	2
#32942	19

Subgroups — C19×#32942 #18038901

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32942 #18038901