Subgroups — C₁₉×#33572 #18039531

Order 4864.

1108 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3551	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3022	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3021	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3018	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2204	C₂	1	4	yes	maximal, complemented
6	C₁₉×#2203	C₂	1	4	yes	maximal, complemented
7	C₁₉×#2135	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2134	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2132	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#585	C₂²	1	1	yes	characteristic
11	C₁₉×#575	—	2	1	no	—
12	C₂×C₁₉×#137	—	2	1	no	—
13	C₂×C₁₉×AGL(1,ℤ/8)	—	2	1	no	—
14	C₁₉×#563	C₂²	1	2	yes	complemented
15	C₁₉×#560	—	2	1	no	—
16	C₁₉×#555	C₂²	1	2	yes	complemented
17	C₁₉×#553	—	2	1	no	—
18	C₁₉×#552	—	2	1	no	—
19	C₁₉×#551	—	2	1	no	—
20	C₁₉×#548	—	2	1	no	—
21	C₁₉×#546	—	2	1	no	—
22	C₁₉×#540	—	2	2	no	—
23	C₁₉×#538	—	2	2	no	—
24	C₁₉×#537	—	2	1	no	—
25	C₁₉×#536	C₂²	1	1	yes	characteristic
26	C₁₉×#535	C₂²	1	1	yes	characteristic
27	C₁₉×#532	C₂²	1	1	yes	characteristic
28	C₁₉×#529	—	2	1	no	—
29	C₁₉×#456	C₂²	1	2	yes	complemented
30	C₁₉×#456	C₂²	1	4	yes	complemented
31	C₁₉×#455	—	2	1	no	—
32	C₁₉×#455	—	2	2	no	—
33	C₁₉×#454	C₂²	1	4	yes	—
34	C₁₉×#454	C₂²	1	2	yes	complemented
35	C₁₉×#453	—	2	1	no	—
36	C₁₉×#453	—	2	2	no	—
37	C₁₉×#421	—	2	1	no	—
38	C₁₉×#421	—	2	1	no	—
39	C₂×C₁₉×#104	—	2	1	no	—
40	C₁₉×#413	C₂²	1	1	yes	characteristic
41	C₁₉×#413	C₂²	1	1	yes	characteristic
42	C₁₉×#413	C₂²	1	1	yes	characteristic
43	C₁₉×#356	C₂²	1	2	yes	complemented
44	C₁₉×#356	C₂²	1	4	yes	complemented
45	C₁₉×#355	C₂²	1	4	yes	complemented
46	C₁₉×#355	C₂²	1	2	yes	complemented
47	C₁₉×2₋¹⁺⁴	—	4	1	no	—
48	C₁₉×2₋¹⁺⁴	C₂³	1	2	yes	—
49	C₁₉×H(5,𝔽₂)	—	2	1	no	—
50	C₁₉×H(5,𝔽₂)	—	2	1	no	—
51	C₁₉×H(5,𝔽₂)	—	2	1	no	—
52	C₁₉×H(5,𝔽₂)	—	4	1	no	—
53	C₂×#41×C₁₉	—	2	1	no	—
54	C₂×#41×C₁₉	—	2	1	no	—
55	C₂×#41×C₁₉	—	2	1	no	—
56	C₂×#41×C₁₉	—	2	1	no	—
57	C₂×#41×C₁₉	—	4	2	no	—
58	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
59	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
60	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
61	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
62	C₁₉×#137	—	2	4	no	—
63	C₁₉×#137	—	2	2	no	—
64	C₁₉×#137	—	4	1	no	—
65	C₁₉×#137	—	4	2	no	—
66	C₁₉×AGL(1,ℤ/8)	—	2	4	no	—
67	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
68	C₁₉×AGL(1,ℤ/8)	—	4	1	no	—
69	C₁₉×AGL(1,ℤ/8)	—	4	2	no	—
70	C₁₉×#135	—	4	2	no	—
71	C₂×Q₁₆×C₁₉	—	4	1	no	—
72	C₂×SD₁₆×C₁₉	—	4	1	no	—
73	C₂×SD₁₆×C₁₉	—	4	1	no	—
74	C₂×D₈×C₁₉	—	4	1	no	—
75	C₂×M₁₆×C₁₉	—	2	1	no	—
76	C₂×M₁₆×C₁₉	—	2	1	no	—
77	C₂×M₁₆×C₁₉	—	2	1	no	—
78	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
79	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
80	C₁₉×#127	D₄	1	1	yes	characteristic
81	C₁₉×#127	D₄	1	2	yes	—
82	C₁₉×#126	—	2	2	no	—
83	C₁₉×#126	—	2	2	no	—
84	C₁₉×#126	—	2	2	no	—
85	C₁₉×#125	—	2	1	no	—
86	C₁₉×#125	—	2	2	no	—
87	C₁₉×#124	—	2	1	no	—
88	C₁₉×#124	—	2	2	no	—
89	C₁₉×#124	D₄	1	1	yes	characteristic
90	C₁₉×#124	D₄	1	2	yes	—
91	C₁₉×#124	C₂³	1	2	yes	—
92	C₁₉×#124	C₂³	1	1	yes	characteristic
93	C₁₉×#123	—	2	2	no	—
94	C₁₉×#123	—	2	2	no	—
95	C₁₉×#123	—	2	2	no	—
96	C₁₉×#123	—	2	1	no	—
97	C₁₉×#123	—	2	1	no	—
98	C₁₉×#123	—	2	2	no	—
99	C₁₉×C₂²⋊Q₈	—	2	1	no	—
100	C₁₉×C₂²⋊Q₈	—	2	2	no	—
101	C₁₉×C₂²⋊Q₈	—	2	2	no	—
102	C₁₉×C₂²⋊Q₈	—	2	1	no	—
103	C₁₉×C₂²⋊Q₈	—	2	1	no	—
104	C₁₉×#121	—	2	2	no	—
105	C₁₉×#121	—	2	2	no	—
106	C₁₉×#121	—	2	1	no	—
107	C₁₉×#121	—	2	2	no	—
108	C₁₉×#121	—	2	2	no	—
109	C₁₉×#121	—	2	1	no	—
110	C₁₉×#121	—	2	1	no	—
111	C₁₉×#121	—	2	2	no	—
112	C₁₉×#121	—	2	2	no	—
113	C₁₉×#121	—	2	1	no	—
114	C₁₉×#121	—	2	1	no	—
115	C₁₉×#120	—	2	2	no	—
116	C₁₉×#120	—	2	1	no	—
117	C₁₉×#120	—	2	1	no	—
118	C₄×Q₈×C₁₉	—	2	1	no	—
119	C₄×D₄×C₁₉	—	2	2	no	—
120	C₄×D₄×C₁₉	—	2	1	no	—
121	C₄×D₄×C₁₉	—	2	2	no	—
122	C₄×D₄×C₁₉	—	2	1	no	—
123	C₄×D₄×C₁₉	—	2	1	no	—
124	C₄×D₄×C₁₉	—	2	2	no	—
125	C₁₉×#117	—	2	2	no	—
126	C₁₉×#117	—	2	2	no	—
127	C₁₉×#117	D₄	1	1	yes	characteristic
128	C₁₉×#117	D₄	1	1	yes	characteristic
129	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
130	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
131	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
132	C₁₉×#104	—	2	2	no	—
133	C₁₉×#104	—	2	2	no	—
134	C₁₉×#104	—	2	4	no	—
135	C₁₉×#104	—	2	4	no	—
136	C₁₉×#101	C₂³	1	2	yes	—
137	C₁₉×#101	C₂³	1	2	yes	—
138	C₁₉×#101	C₂³	1	2	yes	—
139	C₁₉×#100	—	2	1	no	—
140	C₁₉×#100	—	2	1	no	—
141	C₁₉×#100	—	2	1	no	—
142	C₂⁴×C₁₉	—	2	1	no	—
143	#41×C₁₉	—	2	2	no	—
144	#41×C₁₉	—	2	2	no	—
145	#41×C₁₉	—	2	2	no	—
146	#41×C₁₉	—	2	2	no	—
147	#41×C₁₉	—	2	2	no	—
148	#41×C₁₉	—	2	2	no	—
149	#41×C₁₉	—	4	1	no	—
150	#41×C₁₉	—	4	1	no	—
151	#41×C₁₉	—	4	1	no	—
152	#41×C₁₉	—	4	1	no	—
153	#41×C₁₉	—	4	1	no	—
154	#41×C₁₉	—	4	1	no	—
155	#41×C₁₉	—	4	1	no	—
156	#41×C₁₉	—	4	2	no	—
157	#41×C₁₉	—	4	2	no	—
158	#41×C₁₉	—	4	2	no	—
159	#41×C₁₉	—	4	2	no	—
160	#41×C₁₉	—	4	1	no	—
161	#41×C₁₉	—	8	1	no	—
162	#41×C₁₉	—	8	1	no	—
163	C₂×Q₈×C₁₉	—	2	1	no	—
164	C₂×Q₈×C₁₉	—	2	1	no	—
165	C₂×Q₈×C₁₉	—	2	1	no	—
166	C₂×Q₈×C₁₉	—	2	1	no	—
167	C₂×Q₈×C₁₉	—	4	1	no	—
168	C₂×Q₈×C₁₉	—	4	1	no	—
169	C₂×Q₈×C₁₉	—	4	2	no	—
170	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
171	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
172	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
173	C₂×D₄×C₁₉	—	2	1	no	—
174	C₂×D₄×C₁₉	—	2	1	no	—
175	C₂×D₄×C₁₉	—	2	1	no	—
176	C₂×D₄×C₁₉	—	2	2	no	—
177	C₂×D₄×C₁₉	—	2	2	no	—
178	C₂×D₄×C₁₉	—	2	1	no	—
179	C₂×D₄×C₁₉	—	2	2	no	—
180	C₂×D₄×C₁₉	—	2	2	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	—	4	1	no	—
185	C₂×D₄×C₁₉	—	4	1	no	—
186	C₂×D₄×C₁₉	—	4	2	no	—
187	C₂×D₄×C₁₉	—	4	2	no	—
188	C₂×D₄×C₁₉	—	4	2	no	—
189	C₂×D₄×C₁₉	—	4	1	no	—
190	C₂×D₄×C₁₉	—	4	1	no	—
191	C₂×D₄×C₁₉	—	4	1	no	—
192	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
193	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
194	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
195	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
196	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₁₉	—	2	2	no	—
198	C₂²×C₄×C₁₉	—	2	2	no	—
199	C₂²×C₄×C₁₉	—	2	2	no	—
200	C₂²×C₄×C₁₉	—	2	1	no	—
201	C₂²×C₄×C₁₉	—	2	1	no	—
202	C₂²×C₄×C₁₉	—	2	1	no	—
203	C₂²×C₄×C₁₉	—	4	1	no	—
204	C₂²×C₄×C₁₉	—	4	1	no	—
205	C₂²×C₄×C₁₉	—	4	1	no	—
206	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
209	Q₁₆×C₁₉	—	4	4	no	—
210	Q₁₆×C₁₉	—	4	2	no	—
211	SD₁₆×C₁₉	—	4	4	no	—
212	SD₁₆×C₁₉	—	4	2	no	—
213	SD₁₆×C₁₉	—	4	4	no	—
214	SD₁₆×C₁₉	—	4	2	no	—
215	D₈×C₁₉	—	4	4	no	—
216	D₈×C₁₉	—	4	2	no	—
217	M₁₆×C₁₉	—	2	2	no	—
218	M₁₆×C₁₉	—	2	2	no	—
219	M₁₆×C₁₉	—	2	2	no	—
220	M₁₆×C₁₉	—	4	1	no	—
221	M₁₆×C₁₉	—	4	1	no	—
222	M₁₆×C₁₉	—	4	1	no	—
223	C₂×C₈×C₁₉	—	4	1	no	—
224	C₂×C₈×C₁₉	—	4	1	no	—
225	C₂×C₈×C₁₉	—	4	1	no	—
226	C₄⋊C₄×C₁₉	—	2	2	no	—
227	C₄⋊C₄×C₁₉	—	2	2	no	—
228	C₄⋊C₄×C₁₉	—	2	2	no	—
229	C₄⋊C₄×C₁₉	—	2	2	no	—
230	C₄⋊C₄×C₁₉	—	2	2	no	—
231	C₄⋊C₄×C₁₉	—	2	1	no	—
232	C₄⋊C₄×C₁₉	—	2	1	no	—
233	C₄⋊C₄×C₁₉	—	2	2	no	—
234	C₄⋊C₄×C₁₉	—	2	2	no	—
235	C₄⋊C₄×C₁₉	—	2	1	no	—
236	C₄⋊C₄×C₁₉	—	2	1	no	—
237	C₂²⋊C₄×C₁₉	—	2	2	no	—
238	C₂²⋊C₄×C₁₉	—	2	2	no	—
239	C₂²⋊C₄×C₁₉	—	2	2	no	—
240	C₂²⋊C₄×C₁₉	—	2	2	no	—
241	C₂²⋊C₄×C₁₉	—	2	2	no	—
242	C₂²⋊C₄×C₁₉	—	2	1	no	—
243	C₂²⋊C₄×C₁₉	—	2	2	no	—
244	C₂²⋊C₄×C₁₉	—	2	1	no	—
245	C₂²⋊C₄×C₁₉	—	2	1	no	—
246	C₂²⋊C₄×C₁₉	—	2	1	no	—
247	C₂²⋊C₄×C₁₉	—	2	2	no	—
248	C₂²⋊C₄×C₁₉	—	2	1	no	—
249	C₂²⋊C₄×C₁₉	—	2	2	no	—
250	C₂²⋊C₄×C₁₉	—	2	1	no	—
251	C₂²⋊C₄×C₁₉	—	2	2	no	—
252	C₄²×C₁₉	—	2	2	no	—
253	C₄²×C₁₉	—	2	1	no	—
254	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
255	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
256	C₄²×C₁₉	C₂×D₄	1	2	yes	—
257	C₄²×C₁₉	C₂×D₄	1	2	yes	—
258	#33572	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
259	C₂³×C₁₉	—	2	2	no	—
260	C₂³×C₁₉	—	2	1	no	—
261	C₂³×C₁₉	—	4	1	no	—
262	C₂³×C₁₉	—	4	1	no	—
263	C₂³×C₁₉	—	4	1	no	—
264	C₂³×C₁₉	—	8	1	no	—
265	C₂³×C₁₉	—	8	2	no	—
266	C₂³×C₁₉	#120	1	1	yes	characteristic
267	C₂³×C₁₉	#120	1	1	yes	characteristic
268	C₂³×C₁₉	#120	1	1	yes	characteristic
269	Q₈×C₁₉	—	2	2	no	—
270	Q₈×C₁₉	—	2	2	no	—
271	Q₈×C₁₉	—	2	2	no	—
272	Q₈×C₁₉	—	4	1	no	—
273	Q₈×C₁₉	—	4	2	no	—
274	Q₈×C₁₉	—	4	1	no	—
275	Q₈×C₁₉	—	4	1	no	—
276	Q₈×C₁₉	—	4	1	no	—
277	Q₈×C₁₉	—	4	1	no	—
278	D₄×C₁₉	—	2	2	no	—
279	D₄×C₁₉	—	2	2	no	—
280	D₄×C₁₉	—	2	2	no	—
281	D₄×C₁₉	—	4	1	no	—
282	D₄×C₁₉	—	4	1	no	—
283	D₄×C₁₉	—	4	1	no	—
284	D₄×C₁₉	—	4	2	no	—
285	D₄×C₁₉	—	4	1	no	—
286	D₄×C₁₉	—	4	2	no	—
287	D₄×C₁₉	—	4	2	no	—
288	D₄×C₁₉	—	4	2	no	—
289	D₄×C₁₉	—	4	2	no	—
290	D₄×C₁₉	—	4	1	no	—
291	D₄×C₁₉	—	4	1	no	—
292	D₄×C₁₉	—	4	1	no	—
293	D₄×C₁₉	—	8	1	no	—
294	D₄×C₁₉	—	8	2	no	—
295	D₄×C₁₉	—	8	2	no	—
296	D₄×C₁₉	—	8	2	no	—
297	D₄×C₁₉	—	8	1	no	—
298	D₄×C₁₉	—	8	1	no	—
299	D₄×C₁₉	—	8	2	no	—
300	C₂×C₄×C₁₉	—	2	1	no	—
301	C₂×C₄×C₁₉	—	2	1	no	—
302	C₂×C₄×C₁₉	—	2	1	no	—
303	C₂×C₄×C₁₉	—	2	1	no	—
304	C₂×C₄×C₁₉	—	2	1	no	—
305	C₂×C₄×C₁₉	—	2	1	no	—
306	C₂×C₄×C₁₉	—	2	1	no	—
307	C₂×C₄×C₁₉	—	2	2	no	—
308	C₂×C₄×C₁₉	—	2	1	no	—
309	C₂×C₄×C₁₉	—	2	2	no	—
310	C₂×C₄×C₁₉	—	2	2	no	—
311	C₂×C₄×C₁₉	—	2	1	no	—
312	C₂×C₄×C₁₉	—	4	2	no	—
313	C₂×C₄×C₁₉	—	4	2	no	—
314	C₂×C₄×C₁₉	—	4	2	no	—
315	C₂×C₄×C₁₉	—	4	1	no	—
316	C₂×C₄×C₁₉	—	4	1	no	—
317	C₂×C₄×C₁₉	—	4	1	no	—
318	C₂×C₄×C₁₉	—	4	1	no	—
319	C₂×C₄×C₁₉	—	4	1	no	—
320	C₂×C₄×C₁₉	—	4	2	no	—
321	C₂×C₄×C₁₉	—	8	1	no	—
322	C₂×C₄×C₁₉	—	8	2	no	—
323	C₂×C₄×C₁₉	—	8	1	no	—
324	C₂×C₄×C₁₉	—	8	2	no	—
325	C₂×C₄×C₁₉	—	8	2	no	—
326	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
327	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
328	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
329	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
330	C₈×C₁₉	—	4	2	no	—
331	C₈×C₁₉	—	4	2	no	—
332	C₈×C₁₉	—	4	2	no	—
333	#3551	C₂×C₁₉	1	1	yes	characteristic, complemented
334	#3022	C₂×C₁₉	1	1	yes	characteristic, complemented
335	#3021	C₂×C₁₉	1	1	yes	characteristic, complemented
336	#3018	C₂×C₁₉	1	1	yes	characteristic, complemented
337	#2204	C₂×C₁₉	1	4	yes	complemented
338	#2203	C₂×C₁₉	1	4	yes	complemented
339	#2135	C₂×C₁₉	1	1	yes	characteristic, complemented
340	#2134	C₂×C₁₉	1	1	yes	characteristic, complemented
341	#2132	C₂×C₁₉	1	1	yes	characteristic, complemented
342	C₂²×C₁₉	—	2	1	no	—
343	C₂²×C₁₉	—	2	1	no	—
344	C₂²×C₁₉	—	2	1	no	—
345	C₂²×C₁₉	—	4	1	no	—
346	C₂²×C₁₉	—	4	1	no	—
347	C₂²×C₁₉	—	4	1	no	—
348	C₂²×C₁₉	—	4	1	no	—
349	C₂²×C₁₉	—	4	2	no	—
350	C₂²×C₁₉	—	4	1	no	—
351	C₂²×C₁₉	—	4	2	no	—
352	C₂²×C₁₉	—	4	2	no	—
353	C₂²×C₁₉	—	4	1	no	—
354	C₂²×C₁₉	—	4	2	no	—
355	C₂²×C₁₉	—	16	1	no	—
356	C₂²×C₁₉	—	16	1	no	—
357	C₂²×C₁₉	—	16	1	no	—
358	C₂²×C₁₉	—	16	2	no	—
359	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
360	C₄×C₁₉	—	2	1	no	—
361	C₄×C₁₉	—	2	1	no	—
362	C₄×C₁₉	—	2	1	no	—
363	C₄×C₁₉	—	4	1	no	—
364	C₄×C₁₉	—	4	2	no	—
365	C₄×C₁₉	—	4	2	no	—
366	C₄×C₁₉	—	4	1	no	—
367	C₄×C₁₉	—	4	1	no	—
368	C₄×C₁₉	—	4	2	no	—
369	C₄×C₁₉	—	4	2	no	—
370	C₄×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
371	C₄×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
372	#585	C₂²×C₁₉	1	1	yes	characteristic
373	#575	—	2	1	no	—
374	C₂×#137	—	2	1	no	—
375	C₂×AGL(1,ℤ/8)	—	2	1	no	—
376	#563	C₂²×C₁₉	1	2	yes	complemented
377	#560	—	2	1	no	—
378	#555	C₂²×C₁₉	1	2	yes	complemented
379	#553	—	2	1	no	—
380	#552	—	2	1	no	—
381	#551	—	2	1	no	—
382	#548	—	2	1	no	—
383	#546	—	2	1	no	—
384	#540	—	2	2	no	—
385	#538	—	2	2	no	—
386	#537	—	2	1	no	—
387	#536	C₂²×C₁₉	1	1	yes	characteristic
388	#535	C₂²×C₁₉	1	1	yes	characteristic
389	#532	C₂²×C₁₉	1	1	yes	characteristic
390	#529	—	2	1	no	—
391	#456	C₂²×C₁₉	1	2	yes	complemented
392	#456	C₂²×C₁₉	1	4	yes	complemented
393	#455	—	2	1	no	—
394	#455	—	2	2	no	—
395	#454	C₂²×C₁₉	1	4	yes	—
396	#454	C₂²×C₁₉	1	2	yes	complemented
397	#453	—	2	1	no	—
398	#453	—	2	2	no	—
399	#421	—	2	1	no	—
400	#421	—	2	1	no	—
401	C₂×#104	—	2	1	no	—
402	#413	C₂²×C₁₉	1	1	yes	characteristic
403	#413	C₂²×C₁₉	1	1	yes	characteristic
404	#413	C₂²×C₁₉	1	1	yes	characteristic
405	#356	C₂²×C₁₉	1	2	yes	complemented
406	#356	C₂²×C₁₉	1	4	yes	complemented
407	#355	C₂²×C₁₉	1	2	yes	complemented
408	#355	C₂²×C₁₉	1	4	yes	complemented
409	C₂×C₁₉	—	2	1	no	—
410	C₂×C₁₉	—	4	1	no	—
411	C₂×C₁₉	—	4	1	no	—
412	C₂×C₁₉	—	4	1	no	—
413	C₂×C₁₉	—	8	1	no	—
414	C₂×C₁₉	—	8	2	no	—
415	C₂×C₁₉	—	8	2	no	—
416	C₂×C₁₉	C₂×B(4,𝔽₂)	1	1	yes	characteristic
417	2₋¹⁺⁴	—	4	1	no	—
418	2₋¹⁺⁴	C₂³×C₁₉	1	2	yes	—
419	H(5,𝔽₂)	—	2	1	no	—
420	H(5,𝔽₂)	—	2	1	no	—
421	H(5,𝔽₂)	—	2	1	no	—
422	H(5,𝔽₂)	—	4	1	no	—
423	C₂×#41	—	2	1	no	—
424	C₂×#41	—	2	1	no	—
425	C₂×#41	—	2	1	no	—
426	C₂×#41	—	2	1	no	—
427	C₂×#41	—	4	2	no	—
428	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
429	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
430	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
431	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
432	#137	—	2	4	no	—
433	#137	—	2	2	no	—
434	#137	—	4	1	no	—
435	#137	—	4	2	no	—
436	AGL(1,ℤ/8)	—	2	4	no	—
437	AGL(1,ℤ/8)	—	2	2	no	—
438	AGL(1,ℤ/8)	—	4	1	no	—
439	AGL(1,ℤ/8)	—	4	2	no	—
440	#135	—	4	2	no	—
441	C₂×Q₁₆	—	4	1	no	—
442	C₂×SD₁₆	—	4	1	no	—
443	C₂×SD₁₆	—	4	1	no	—
444	C₂×D₈	—	4	1	no	—
445	C₂×M₁₆	—	2	1	no	—
446	C₂×M₁₆	—	2	1	no	—
447	C₂×M₁₆	—	2	1	no	—
448	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
449	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
450	#127	D₄×C₁₉	1	1	yes	characteristic
451	#127	D₄×C₁₉	1	2	yes	—
452	#126	—	2	2	no	—
453	#126	—	2	2	no	—
454	#126	—	2	2	no	—
455	#125	—	2	1	no	—
456	#125	—	2	2	no	—
457	#124	—	2	1	no	—
458	#124	—	2	2	no	—
459	#124	D₄×C₁₉	1	1	yes	characteristic
460	#124	D₄×C₁₉	1	2	yes	—
461	#124	C₂³×C₁₉	1	1	yes	characteristic
462	#124	C₂³×C₁₉	1	2	yes	—
463	#123	—	2	2	no	—
464	#123	—	2	2	no	—
465	#123	—	2	2	no	—
466	#123	—	2	1	no	—
467	#123	—	2	1	no	—
468	#123	—	2	2	no	—
469	C₂²⋊Q₈	—	2	1	no	—
470	C₂²⋊Q₈	—	2	2	no	—
471	C₂²⋊Q₈	—	2	2	no	—
472	C₂²⋊Q₈	—	2	1	no	—
473	C₂²⋊Q₈	—	2	1	no	—
474	#121	—	2	2	no	—
475	#121	—	2	2	no	—
476	#121	—	2	1	no	—
477	#121	—	2	2	no	—
478	#121	—	2	2	no	—
479	#121	—	2	1	no	—
480	#121	—	2	1	no	—
481	#121	—	2	2	no	—
482	#121	—	2	2	no	—
483	#121	—	2	1	no	—
484	#121	—	2	1	no	—
485	#120	—	2	2	no	—
486	#120	—	2	1	no	—
487	#120	—	2	1	no	—
488	C₄×Q₈	—	2	1	no	—
489	C₄×D₄	—	2	2	no	—
490	C₄×D₄	—	2	1	no	—
491	C₄×D₄	—	2	2	no	—
492	C₄×D₄	—	2	1	no	—
493	C₄×D₄	—	2	1	no	—
494	C₄×D₄	—	2	2	no	—
495	#117	—	2	2	no	—
496	#117	—	2	2	no	—
497	#117	D₄×C₁₉	1	1	yes	characteristic
498	#117	D₄×C₁₉	1	1	yes	characteristic
499	C₂×C₄⋊C₄	—	2	1	no	—
500	C₂×C₂²⋊C₄	—	2	2	no	—
501	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
502	#104	—	2	2	no	—
503	#104	—	2	2	no	—
504	#104	—	2	4	no	—
505	#104	—	2	4	no	—
506	#101	C₂³×C₁₉	1	2	yes	—
507	#101	C₂³×C₁₉	1	2	yes	—
508	#101	C₂³×C₁₉	1	2	yes	—
509	#100	—	2	1	no	—
510	#100	—	2	1	no	—
511	#100	—	2	1	no	—
512	C₁₉	#33572	1	1	yes	characteristic, direct product factor, Sylow
513	C₂⁴	—	2	1	no	—
514	#41	—	2	2	no	—
515	#41	—	2	2	no	—
516	#41	—	2	2	no	—
517	#41	—	2	2	no	—
518	#41	—	2	2	no	—
519	#41	—	2	2	no	—
520	#41	—	4	1	no	—
521	#41	—	4	1	no	—
522	#41	—	4	1	no	—
523	#41	—	4	1	no	—
524	#41	—	4	1	no	—
525	#41	—	4	1	no	—
526	#41	—	4	1	no	—
527	#41	—	4	2	no	—
528	#41	—	4	2	no	—
529	#41	—	4	2	no	—
530	#41	—	4	2	no	—
531	#41	—	4	1	no	—
532	#41	—	8	1	no	—
533	#41	—	8	1	no	—
534	C₂×Q₈	—	2	1	no	—
535	C₂×Q₈	—	2	1	no	—
536	C₂×Q₈	—	2	1	no	—
537	C₂×Q₈	—	2	1	no	—
538	C₂×Q₈	—	4	1	no	—
539	C₂×Q₈	—	4	1	no	—
540	C₂×Q₈	—	4	2	no	—
541	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
542	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
543	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
544	C₂×D₄	—	2	1	no	—
545	C₂×D₄	—	2	1	no	—
546	C₂×D₄	—	2	1	no	—
547	C₂×D₄	—	2	2	no	—
548	C₂×D₄	—	2	2	no	—
549	C₂×D₄	—	2	1	no	—
550	C₂×D₄	—	2	2	no	—
551	C₂×D₄	—	2	2	no	—
552	C₂×D₄	—	2	1	no	—
553	C₂×D₄	—	2	1	no	—
554	C₂×D₄	—	2	1	no	—
555	C₂×D₄	—	4	1	no	—
556	C₂×D₄	—	4	1	no	—
557	C₂×D₄	—	4	2	no	—
558	C₂×D₄	—	4	2	no	—
559	C₂×D₄	—	4	2	no	—
560	C₂×D₄	—	4	1	no	—
561	C₂×D₄	—	4	1	no	—
562	C₂×D₄	—	4	1	no	—
563	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
564	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
565	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
566	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
567	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
568	C₂²×C₄	—	2	2	no	—
569	C₂²×C₄	—	2	2	no	—
570	C₂²×C₄	—	2	2	no	—
571	C₂²×C₄	—	2	1	no	—
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	4	1	no	—
575	C₂²×C₄	—	4	1	no	—
576	C₂²×C₄	—	4	1	no	—
577	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
578	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
579	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
580	Q₁₆	—	4	4	no	—
581	Q₁₆	—	4	2	no	—
582	SD₁₆	—	4	4	no	—
583	SD₁₆	—	4	2	no	—
584	SD₁₆	—	4	4	no	—
585	SD₁₆	—	4	2	no	—
586	D₈	—	4	4	no	—
587	D₈	—	4	2	no	—
588	M₁₆	—	2	2	no	—
589	M₁₆	—	2	2	no	—
590	M₁₆	—	2	2	no	—
591	M₁₆	—	4	1	no	—
592	M₁₆	—	4	1	no	—
593	M₁₆	—	4	1	no	—
594	C₂×C₈	—	4	1	no	—
595	C₂×C₈	—	4	1	no	—
596	C₂×C₈	—	4	1	no	—
597	C₄⋊C₄	—	2	2	no	—
598	C₄⋊C₄	—	2	2	no	—
599	C₄⋊C₄	—	2	2	no	—
600	C₄⋊C₄	—	2	2	no	—
601	C₄⋊C₄	—	2	2	no	—
602	C₄⋊C₄	—	2	1	no	—
603	C₄⋊C₄	—	2	1	no	—
604	C₄⋊C₄	—	2	2	no	—
605	C₄⋊C₄	—	2	2	no	—
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	—	2	1	no	—
608	C₂²⋊C₄	—	2	2	no	—
609	C₂²⋊C₄	—	2	2	no	—
610	C₂²⋊C₄	—	2	2	no	—
611	C₂²⋊C₄	—	2	2	no	—
612	C₂²⋊C₄	—	2	2	no	—
613	C₂²⋊C₄	—	2	1	no	—
614	C₂²⋊C₄	—	2	2	no	—
615	C₂²⋊C₄	—	2	1	no	—
616	C₂²⋊C₄	—	2	1	no	—
617	C₂²⋊C₄	—	2	1	no	—
618	C₂²⋊C₄	—	2	2	no	—
619	C₂²⋊C₄	—	2	1	no	—
620	C₂²⋊C₄	—	2	2	no	—
621	C₂²⋊C₄	—	2	1	no	—
622	C₂²⋊C₄	—	2	2	no	—
623	C₄²	—	2	2	no	—
624	C₄²	—	2	1	no	—
625	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
626	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
627	C₄²	C₂×D₄×C₁₉	1	2	yes	—
628	C₄²	C₂×D₄×C₁₉	1	2	yes	—
629	C₂³	—	2	2	no	—
630	C₂³	—	2	1	no	—
631	C₂³	—	4	1	no	—
632	C₂³	—	4	1	no	—
633	C₂³	—	4	1	no	—
634	C₂³	—	8	1	no	—
635	C₂³	—	8	2	no	—
636	C₂³	C₁₉×#120	1	1	yes	characteristic
637	C₂³	C₁₉×#120	1	1	yes	characteristic
638	C₂³	C₁₉×#120	1	1	yes	characteristic
639	Q₈	—	2	2	no	—
640	Q₈	—	2	2	no	—
641	Q₈	—	2	2	no	—
642	Q₈	—	4	1	no	—
643	Q₈	—	4	2	no	—
644	Q₈	—	4	1	no	—
645	Q₈	—	4	1	no	—
646	Q₈	—	4	1	no	—
647	Q₈	—	4	1	no	—
648	D₄	—	2	2	no	—
649	D₄	—	2	2	no	—
650	D₄	—	2	2	no	—
651	D₄	—	4	1	no	—
652	D₄	—	4	1	no	—
653	D₄	—	4	1	no	—
654	D₄	—	4	2	no	—
655	D₄	—	4	1	no	—
656	D₄	—	4	2	no	—
657	D₄	—	4	2	no	—
658	D₄	—	4	2	no	—
659	D₄	—	4	2	no	—
660	D₄	—	4	1	no	—
661	D₄	—	4	1	no	—
662	D₄	—	4	1	no	—
663	D₄	—	8	1	no	—
664	D₄	—	8	2	no	—
665	D₄	—	8	2	no	—
666	D₄	—	8	2	no	—
667	D₄	—	8	2	no	—
668	D₄	—	8	1	no	—
669	D₄	—	8	1	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	4	2	no	—
683	C₂×C₄	—	4	2	no	—
684	C₂×C₄	—	4	2	no	—
685	C₂×C₄	—	4	1	no	—
686	C₂×C₄	—	4	1	no	—
687	C₂×C₄	—	4	1	no	—
688	C₂×C₄	—	4	1	no	—
689	C₂×C₄	—	4	1	no	—
690	C₂×C₄	—	4	2	no	—
691	C₂×C₄	—	8	1	no	—
692	C₂×C₄	—	8	2	no	—
693	C₂×C₄	—	8	2	no	—
694	C₂×C₄	—	8	1	no	—
695	C₂×C₄	—	8	2	no	—
696	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
697	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
698	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
699	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
700	C₈	—	4	2	no	—
701	C₈	—	4	2	no	—
702	C₈	—	4	2	no	—
703	C₂²	—	2	1	no	—
704	C₂²	—	2	1	no	—
705	C₂²	—	2	1	no	—
706	C₂²	—	4	1	no	—
707	C₂²	—	4	1	no	—
708	C₂²	—	4	1	no	—
709	C₂²	—	4	1	no	—
710	C₂²	—	4	2	no	—
711	C₂²	—	4	1	no	—
712	C₂²	—	4	2	no	—
713	C₂²	—	4	2	no	—
714	C₂²	—	4	1	no	—
715	C₂²	—	4	2	no	—
716	C₂²	—	16	1	no	—
717	C₂²	—	16	1	no	—
718	C₂²	—	16	1	no	—
719	C₂²	—	16	2	no	—
720	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
721	C₄	—	2	1	no	—
722	C₄	—	2	1	no	—
723	C₄	—	2	1	no	—
724	C₄	—	4	1	no	—
725	C₄	—	4	2	no	—
726	C₄	—	4	2	no	—
727	C₄	—	4	1	no	—
728	C₄	—	4	1	no	—
729	C₄	—	4	2	no	—
730	C₄	—	4	2	no	—
731	C₄	C₁₉×B(4,𝔽₂)	1	1	yes	characteristic
732	C₄	C₁₉×B(4,𝔽₂)	1	1	yes	characteristic
733	C₂	—	2	1	no	—
734	C₂	—	4	1	no	—
735	C₂	—	4	1	no	—
736	C₂	—	4	1	no	—
737	C₂	—	8	2	no	—
738	C₂	—	8	1	no	—
739	C₂	—	8	2	no	—
740	C₂	C₂×C₁₉×B(4,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₉	C₂×B(4,𝔽₂)
commutator, Frattini, cosocle	C₂×Q₈	C₂⁴×C₁₉
LCS	G ▷ C₂×Q₈ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂×#41×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3551	C₂	semidirect
2. C₁₉×#3022	C₂	semidirect
3. C₁₉×#3021	C₂	semidirect
4. C₁₉×#3018	C₂	semidirect
5. C₁₉×#2204	C₂	semidirect
6. C₁₉×#2203	C₂	semidirect
7. C₁₉×#2135	C₂	semidirect
8. C₁₉×#2134	C₂	semidirect
9. C₁₉×#2132	C₂	semidirect
14. C₁₉×#563	C₂²	semidirect
16. C₁₉×#555	C₂²	semidirect
29. C₁₉×#456	C₂²	semidirect
30. C₁₉×#456	C₂²	semidirect
34. C₁₉×#454	C₂²	semidirect
43. C₁₉×#356	C₂²	semidirect
44. C₁₉×#356	C₂²	semidirect
45. C₁₉×#355	C₂²	semidirect
46. C₁₉×#355	C₂²	semidirect
258. #33572	C₁₉	direct (N × H)
333. #3551	C₂×C₁₉	semidirect
334. #3022	C₂×C₁₉	semidirect
335. #3021	C₂×C₁₉	semidirect
336. #3018	C₂×C₁₉	semidirect
337. #2204	C₂×C₁₉	semidirect
338. #2203	C₂×C₁₉	semidirect
339. #2135	C₂×C₁₉	semidirect
340. #2134	C₂×C₁₉	semidirect
341. #2132	C₂×C₁₉	semidirect
376. #563	C₂²×C₁₉	semidirect
378. #555	C₂²×C₁₉	semidirect
391. #456	C₂²×C₁₉	semidirect
392. #456	C₂²×C₁₉	semidirect
396. #454	C₂²×C₁₉	semidirect
405. #356	C₂²×C₁₉	semidirect
406. #356	C₂²×C₁₉	semidirect
407. #355	C₂²×C₁₉	semidirect
408. #355	C₂²×C₁₉	semidirect
512. C₁₉	#33572	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×#3551	2
C₁₉×#3022	2
C₁₉×#3021	2
C₁₉×#3018	2
C₁₉×#2204	2
C₁₉×#2203	2
C₁₉×#2135	2
C₁₉×#2134	2
C₁₉×#2132	2
#33572	19

Subgroups — C19×#33572 #18039531

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#33572 #18039531