Subgroups — C₁₉×#18934 #18024893

Order 4864.

1020 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3549	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3245	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3214	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3207	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1646	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1639	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1624	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1619	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1551	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1496	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1480	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×H(3,𝔽₄)	—	2	2	no	—
13	C₁₉×#555	—	2	1	no	—
14	C₁₉×#555	—	2	1	no	—
15	C₁₉×#555	C₂²	1	2	yes	—
16	D₄²×C₁₉	—	2	1	no	—
17	D₄²×C₁₉	—	2	1	no	—
18	D₄²×C₁₉	C₂²	1	2	yes	—
19	C₁₉×#535	—	2	2	no	—
20	C₁₉×#535	—	2	2	no	—
21	C₁₉×#535	—	2	2	no	—
22	C₁₉×#532	C₂²	1	1	yes	characteristic
23	C₁₉×#532	C₂²	1	1	yes	characteristic
24	C₁₉×#532	C₂²	1	1	yes	characteristic
25	C₁₉×#532	C₂²	1	1	yes	characteristic, complemented
26	C₁₉×#496	—	2	1	no	—
27	C₁₉×#493	C₂²	1	1	yes	characteristic
28	C₁₉×#492	C₂²	1	1	yes	characteristic, complemented
29	C₁₉×#489	—	2	1	no	—
30	C₁₉×#487	C₂²	1	1	yes	characteristic, complemented
31	C₁₉×#486	C₂²	1	1	yes	characteristic
32	C₁₉×#474	—	2	1	no	—
33	C₁₉×#474	C₂²	1	2	yes	complemented
34	C₁₉×#466	—	2	2	no	—
35	C₁₉×#463	—	2	2	no	—
36	C₁₉×#461	C₂²	1	2	yes	complemented
37	C₁₉×#459	—	2	1	no	—
38	C₁₉×#459	C₂²	1	2	yes	complemented
39	C₁₉×#459	C₂²	1	2	yes	complemented
40	C₁₉×#449	—	2	2	no	—
41	C₁₉×#449	—	2	2	no	—
42	C₁₉×#432	C₂²	1	1	yes	characteristic, complemented
43	C₁₉×#431	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
45	C₁₉×#333	C₂²	1	2	yes	complemented
46	C₁₉×#331	C₂²	1	2	yes	—
47	C₁₉×D₄⋊C₈	C₂²	1	2	yes	complemented
48	C₁₉×D₄⋊C₈	C₂²	1	2	yes	complemented
49	C₁₉×D₄⋊C₈	C₂²	1	2	yes	complemented
50	C₁₉×D₄⋊C₈	C₂²	1	2	yes	complemented
51	C₂×#41×C₁₉	—	2	1	no	—
52	C₂×#41×C₁₉	—	2	1	no	—
53	C₂×#41×C₁₉	—	2	1	no	—
54	C₂×#41×C₁₉	D₄	1	2	yes	—
55	C₂²×D₄×C₁₉	—	2	2	no	—
56	C₂²×D₄×C₁₉	—	2	2	no	—
57	C₂²×D₄×C₁₉	—	2	2	no	—
58	C₂×SD₁₆×C₁₉	—	2	2	no	—
59	C₂×SD₁₆×C₁₉	—	2	2	no	—
60	C₂×D₈×C₁₉	—	2	2	no	—
61	C₂×D₈×C₁₉	—	2	2	no	—
62	C₂×D₈×C₁₉	—	2	2	no	—
63	C₂²×C₈×C₁₉	—	2	1	no	—
64	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
65	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
66	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
67	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
68	C₁₉×#127	—	2	4	no	—
69	C₁₉×#127	D₄	1	1	yes	characteristic
70	C₁₉×#127	D₄	1	1	yes	characteristic
71	C₁₉×#127	C₂³	1	1	yes	characteristic
72	C₁₉×#127	C₂³	1	1	yes	characteristic
73	C₁₉×#124	—	2	4	no	—
74	C₁₉×#124	—	2	4	no	—
75	C₁₉×#124	—	2	4	no	—
76	C₁₉×#124	—	2	1	no	—
77	C₁₉×#124	—	2	1	no	—
78	C₁₉×#124	—	2	1	no	—
79	C₁₉×#124	D₄	1	2	yes	—
80	C₁₉×#121	—	2	2	no	—
81	C₁₉×#121	—	2	2	no	—
82	C₁₉×#121	—	2	2	no	—
83	C₁₉×#121	—	2	2	no	—
84	C₁₉×#121	—	2	1	no	—
85	C₁₉×#121	—	2	1	no	—
86	C₁₉×#121	—	2	1	no	—
87	C₁₉×#121	—	2	1	no	—
88	C₁₉×#121	—	2	2	no	—
89	C₁₉×#121	—	2	2	no	—
90	C₁₉×#121	—	2	1	no	—
91	C₁₉×#121	—	2	1	no	—
92	C₁₉×#121	D₄	1	2	yes	—
93	C₁₉×#121	D₄	1	2	yes	—
94	C₁₉×#120	—	2	4	no	—
95	C₁₉×#120	—	2	4	no	—
96	C₁₉×#120	—	2	4	no	—
97	C₁₉×#120	—	2	4	no	—
98	C₄×D₄×C₁₉	—	2	1	no	—
99	C₄×D₄×C₁₉	—	2	1	no	—
100	C₄×D₄×C₁₉	—	2	1	no	—
101	C₄×D₄×C₁₉	—	2	1	no	—
102	C₄×D₄×C₁₉	—	2	1	no	—
103	C₄×D₄×C₁₉	—	2	1	no	—
104	C₄×D₄×C₁₉	C₂³	1	2	yes	—
105	C₄×D₄×C₁₉	C₂³	1	2	yes	—
106	C₁₉×#117	—	2	2	no	—
107	C₁₉×#117	—	2	2	no	—
108	C₁₉×#117	—	2	2	no	—
109	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
110	C₁₉×#107	—	2	2	no	—
111	C₁₉×C₄⋊C₈	—	2	1	no	—
112	C₁₉×C₄⋊C₈	—	2	1	no	—
113	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
114	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
115	C₁₉×#103	—	2	2	no	—
116	C₁₉×#103	—	2	2	no	—
117	C₁₉×#102	—	2	2	no	—
118	C₁₉×#102	—	2	2	no	—
119	C₁₉×#102	—	2	2	no	—
120	C₁₉×#102	—	2	2	no	—
121	C₁₉×C₂²⋊C₈	—	2	1	no	—
122	C₁₉×C₂²⋊C₈	—	2	1	no	—
123	C₁₉×#97	—	2	1	no	—
124	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
125	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
126	C₂⁴×C₁₉	—	2	4	no	—
127	#41×C₁₉	—	8	1	no	—
128	#41×C₁₉	—	8	2	no	—
129	#41×C₁₉	—	8	1	no	—
130	#41×C₁₉	—	8	2	no	—
131	#41×C₁₉	—	8	2	no	—
132	C₂×Q₈×C₁₉	—	2	1	no	—
133	C₂×Q₈×C₁₉	—	2	1	no	—
134	C₂×Q₈×C₁₉	—	2	1	no	—
135	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
136	C₂×D₄×C₁₉	—	2	4	no	—
137	C₂×D₄×C₁₉	—	2	4	no	—
138	C₂×D₄×C₁₉	—	2	4	no	—
139	C₂×D₄×C₁₉	—	2	2	no	—
140	C₂×D₄×C₁₉	—	2	2	no	—
141	C₂×D₄×C₁₉	—	2	2	no	—
142	C₂×D₄×C₁₉	—	2	1	no	—
143	C₂×D₄×C₁₉	—	2	1	no	—
144	C₂×D₄×C₁₉	—	2	1	no	—
145	C₂×D₄×C₁₉	—	2	1	no	—
146	C₂×D₄×C₁₉	—	2	1	no	—
147	C₂×D₄×C₁₉	—	2	1	no	—
148	C₂×D₄×C₁₉	—	2	1	no	—
149	C₂×D₄×C₁₉	—	2	1	no	—
150	C₂×D₄×C₁₉	—	2	1	no	—
151	C₂×D₄×C₁₉	—	4	1	no	—
152	C₂×D₄×C₁₉	—	8	2	no	—
153	C₂×D₄×C₁₉	—	8	2	no	—
154	C₂×D₄×C₁₉	—	8	2	no	—
155	C₂×D₄×C₁₉	—	8	2	no	—
156	C₂×D₄×C₁₉	—	8	4	no	—
157	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
158	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
159	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
160	C₂²×C₄×C₁₉	—	2	2	no	—
161	C₂²×C₄×C₁₉	—	2	2	no	—
162	C₂²×C₄×C₁₉	—	2	2	no	—
163	C₂²×C₄×C₁₉	—	4	1	no	—
164	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
167	SD₁₆×C₁₉	—	8	2	no	—
168	SD₁₆×C₁₉	—	8	2	no	—
169	D₈×C₁₉	—	8	2	no	—
170	D₈×C₁₉	—	8	2	no	—
171	D₈×C₁₉	—	8	2	no	—
172	C₂×C₈×C₁₉	—	2	2	no	—
173	C₂×C₈×C₁₉	—	2	1	no	—
174	C₂×C₈×C₁₉	—	2	2	no	—
175	C₂×C₈×C₁₉	—	2	1	no	—
176	C₂×C₈×C₁₉	—	8	1	no	—
177	C₄⋊C₄×C₁₉	—	2	1	no	—
178	C₄⋊C₄×C₁₉	—	2	1	no	—
179	C₄⋊C₄×C₁₉	—	2	1	no	—
180	C₄⋊C₄×C₁₉	—	2	1	no	—
181	C₄⋊C₄×C₁₉	—	2	1	no	—
182	C₄⋊C₄×C₁₉	—	2	1	no	—
183	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
184	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
185	C₂²⋊C₄×C₁₉	—	2	4	no	—
186	C₂²⋊C₄×C₁₉	—	2	4	no	—
187	C₂²⋊C₄×C₁₉	—	2	4	no	—
188	C₂²⋊C₄×C₁₉	—	2	2	no	—
189	C₂²⋊C₄×C₁₉	—	2	2	no	—
190	C₂²⋊C₄×C₁₉	—	2	2	no	—
191	C₂²⋊C₄×C₁₉	—	2	2	no	—
192	C₂²⋊C₄×C₁₉	—	2	2	no	—
193	C₂²⋊C₄×C₁₉	—	2	2	no	—
194	C₂²⋊C₄×C₁₉	—	4	1	no	—
195	C₂²⋊C₄×C₁₉	—	4	1	no	—
196	C₄²×C₁₉	—	2	4	no	—
197	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
198	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
199	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
200	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
201	#18934	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
202	C₂³×C₁₉	—	2	2	no	—
203	C₂³×C₁₉	—	2	2	no	—
204	C₂³×C₁₉	—	2	2	no	—
205	C₂³×C₁₉	—	4	1	no	—
206	C₂³×C₁₉	—	8	4	no	—
207	C₂³×C₁₉	—	8	4	no	—
208	C₂³×C₁₉	—	8	4	no	—
209	C₂³×C₁₉	#120	1	1	yes	characteristic
210	Q₈×C₁₉	—	4	2	no	—
211	Q₈×C₁₉	—	4	2	no	—
212	Q₈×C₁₉	—	8	1	no	—
213	Q₈×C₁₉	—	8	1	no	—
214	D₄×C₁₉	—	2	2	no	—
215	D₄×C₁₉	—	2	2	no	—
216	D₄×C₁₉	—	2	2	no	—
217	D₄×C₁₉	—	2	2	no	—
218	D₄×C₁₉	—	4	2	no	—
219	D₄×C₁₉	—	4	2	no	—
220	D₄×C₁₉	—	4	2	no	—
221	D₄×C₁₉	—	4	2	no	—
222	D₄×C₁₉	—	4	2	no	—
223	D₄×C₁₉	—	4	1	no	—
224	D₄×C₁₉	—	4	1	no	—
225	D₄×C₁₉	—	4	2	no	—
226	D₄×C₁₉	—	4	1	no	—
227	D₄×C₁₉	—	4	1	no	—
228	D₄×C₁₉	—	8	1	no	—
229	D₄×C₁₉	—	8	1	no	—
230	D₄×C₁₉	—	8	2	no	—
231	D₄×C₁₉	—	8	2	no	—
232	D₄×C₁₉	—	8	2	no	—
233	D₄×C₁₉	—	8	4	no	—
234	D₄×C₁₉	—	8	4	no	—
235	D₄×C₁₉	—	8	4	no	—
236	D₄×C₁₉	—	8	2	no	—
237	C₂×C₄×C₁₉	—	2	1	no	—
238	C₂×C₄×C₁₉	—	2	2	no	—
239	C₂×C₄×C₁₉	—	2	1	no	—
240	C₂×C₄×C₁₉	—	2	2	no	—
241	C₂×C₄×C₁₉	—	2	2	no	—
242	C₂×C₄×C₁₉	—	2	2	no	—
243	C₂×C₄×C₁₉	—	4	1	no	—
244	C₂×C₄×C₁₉	—	4	4	no	—
245	C₂×C₄×C₁₉	—	4	2	no	—
246	C₂×C₄×C₁₉	—	4	2	no	—
247	C₂×C₄×C₁₉	—	4	2	no	—
248	C₂×C₄×C₁₉	—	4	2	no	—
249	C₂×C₄×C₁₉	—	4	1	no	—
250	C₂×C₄×C₁₉	—	8	2	no	—
251	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
252	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
253	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
254	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
255	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
257	C₈×C₁₉	—	4	1	no	—
258	C₈×C₁₉	—	4	1	no	—
259	C₈×C₁₉	—	4	2	no	—
260	C₈×C₁₉	—	4	2	no	—
261	#3549	C₂×C₁₉	1	1	yes	characteristic, complemented
262	#3245	C₂×C₁₉	1	1	yes	characteristic, complemented
263	#3214	C₂×C₁₉	1	1	yes	characteristic, complemented
264	#3207	C₂×C₁₉	1	1	yes	characteristic, complemented
265	#1646	C₂×C₁₉	1	2	yes	complemented
266	#1639	C₂×C₁₉	1	2	yes	complemented
267	#1624	C₂×C₁₉	1	2	yes	complemented
268	#1619	C₂×C₁₉	1	2	yes	complemented
269	#1551	C₂×C₁₉	1	1	yes	characteristic, complemented
270	#1496	C₂×C₁₉	1	1	yes	characteristic, complemented
271	#1480	C₂×C₁₉	1	1	yes	characteristic, complemented
272	C₂²×C₁₉	—	2	1	no	—
273	C₂²×C₁₉	—	2	1	no	—
274	C₂²×C₁₉	—	2	1	no	—
275	C₂²×C₁₉	—	4	2	no	—
276	C₂²×C₁₉	—	4	2	no	—
277	C₂²×C₁₉	—	4	2	no	—
278	C₂²×C₁₉	—	4	2	no	—
279	C₂²×C₁₉	—	4	2	no	—
280	C₂²×C₁₉	—	4	2	no	—
281	C₂²×C₁₉	—	4	2	no	—
282	C₂²×C₁₉	—	4	2	no	—
283	C₂²×C₁₉	—	4	2	no	—
284	C₂²×C₁₉	—	8	1	no	—
285	C₂²×C₁₉	—	8	1	no	—
286	C₂²×C₁₉	—	8	1	no	—
287	C₂²×C₁₉	—	16	8	no	—
288	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
289	C₄×C₁₉	—	2	1	no	—
290	C₄×C₁₉	—	2	1	no	—
291	C₄×C₁₉	—	2	1	no	—
292	C₄×C₁₉	—	2	1	no	—
293	C₄×C₁₉	—	4	2	no	—
294	C₄×C₁₉	—	4	2	no	—
295	C₄×C₁₉	—	4	2	no	—
296	C₄×C₁₉	—	8	1	no	—
297	C₄×C₁₉	#576	1	2	yes	—
298	C₄×C₁₉	#576	1	1	yes	characteristic
299	C₄×C₁₉	#577	1	1	yes	characteristic
300	H(3,𝔽₄)	—	2	2	no	—
301	#555	—	2	1	no	—
302	#555	—	2	1	no	—
303	#555	C₂²×C₁₉	1	2	yes	—
304	D₄²	—	2	1	no	—
305	D₄²	—	2	1	no	—
306	D₄²	C₂²×C₁₉	1	2	yes	—
307	#535	—	2	2	no	—
308	#535	—	2	2	no	—
309	#535	—	2	2	no	—
310	#532	C₂²×C₁₉	1	1	yes	characteristic
311	#532	C₂²×C₁₉	1	1	yes	characteristic
312	#532	C₂²×C₁₉	1	1	yes	characteristic
313	#532	C₂²×C₁₉	1	1	yes	characteristic, complemented
314	#496	—	2	1	no	—
315	#493	C₂²×C₁₉	1	1	yes	characteristic
316	#492	C₂²×C₁₉	1	1	yes	characteristic, complemented
317	#489	—	2	1	no	—
318	#487	C₂²×C₁₉	1	1	yes	characteristic, complemented
319	#486	C₂²×C₁₉	1	1	yes	characteristic
320	#474	—	2	1	no	—
321	#474	C₂²×C₁₉	1	2	yes	complemented
322	#466	—	2	2	no	—
323	#463	—	2	2	no	—
324	#461	C₂²×C₁₉	1	2	yes	complemented
325	#459	—	2	1	no	—
326	#459	C₂²×C₁₉	1	2	yes	complemented
327	#459	C₂²×C₁₉	1	2	yes	complemented
328	#449	—	2	2	no	—
329	#449	—	2	2	no	—
330	#432	C₂²×C₁₉	1	1	yes	characteristic, complemented
331	#431	C₂²×C₁₉	1	1	yes	characteristic, complemented
332	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
333	#333	C₂²×C₁₉	1	2	yes	complemented
334	#331	C₂²×C₁₉	1	2	yes	—
335	D₄⋊C₈	C₂²×C₁₉	1	2	yes	complemented
336	D₄⋊C₈	C₂²×C₁₉	1	2	yes	complemented
337	D₄⋊C₈	C₂²×C₁₉	1	2	yes	complemented
338	D₄⋊C₈	C₂²×C₁₉	1	2	yes	complemented
339	C₂×C₁₉	—	4	1	no	—
340	C₂×C₁₉	—	8	2	no	—
341	C₂×C₁₉	—	8	2	no	—
342	C₂×C₁₉	—	8	2	no	—
343	C₂×C₁₉	—	16	1	no	—
344	C₂×C₁₉	#3008	1	1	yes	characteristic
345	C₂×C₁₉	#3012	1	1	yes	characteristic
346	C₂×C₁₉	#3019	1	1	yes	characteristic
347	C₂×#41	—	2	1	no	—
348	C₂×#41	—	2	1	no	—
349	C₂×#41	—	2	1	no	—
350	C₂×#41	D₄×C₁₉	1	2	yes	—
351	C₂²×D₄	—	2	2	no	—
352	C₂²×D₄	—	2	2	no	—
353	C₂²×D₄	—	2	2	no	—
354	C₂×SD₁₆	—	2	2	no	—
355	C₂×SD₁₆	—	2	2	no	—
356	C₂×D₈	—	2	2	no	—
357	C₂×D₈	—	2	2	no	—
358	C₂×D₈	—	2	2	no	—
359	C₂²×C₈	—	2	1	no	—
360	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
361	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
362	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
363	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
364	#127	—	2	4	no	—
365	#127	D₄×C₁₉	1	1	yes	characteristic
366	#127	D₄×C₁₉	1	1	yes	characteristic
367	#127	C₂³×C₁₉	1	1	yes	characteristic
368	#127	C₂³×C₁₉	1	1	yes	characteristic
369	#124	—	2	4	no	—
370	#124	—	2	4	no	—
371	#124	—	2	4	no	—
372	#124	—	2	1	no	—
373	#124	—	2	1	no	—
374	#124	—	2	1	no	—
375	#124	D₄×C₁₉	1	2	yes	—
376	#121	—	2	2	no	—
377	#121	—	2	2	no	—
378	#121	—	2	2	no	—
379	#121	—	2	2	no	—
380	#121	—	2	1	no	—
381	#121	—	2	1	no	—
382	#121	—	2	1	no	—
383	#121	—	2	1	no	—
384	#121	—	2	2	no	—
385	#121	—	2	2	no	—
386	#121	—	2	1	no	—
387	#121	—	2	1	no	—
388	#121	D₄×C₁₉	1	2	yes	—
389	#121	D₄×C₁₉	1	2	yes	—
390	#120	—	2	4	no	—
391	#120	—	2	4	no	—
392	#120	—	2	4	no	—
393	#120	—	2	4	no	—
394	C₄×D₄	—	2	1	no	—
395	C₄×D₄	—	2	1	no	—
396	C₄×D₄	—	2	1	no	—
397	C₄×D₄	—	2	1	no	—
398	C₄×D₄	—	2	1	no	—
399	C₄×D₄	—	2	1	no	—
400	C₄×D₄	C₂³×C₁₉	1	2	yes	—
401	C₄×D₄	C₂³×C₁₉	1	2	yes	—
402	#117	—	2	2	no	—
403	#117	—	2	2	no	—
404	#117	—	2	2	no	—
405	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
406	#107	—	2	2	no	—
407	C₄⋊C₈	—	2	1	no	—
408	C₄⋊C₈	—	2	1	no	—
409	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
410	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
411	#103	—	2	2	no	—
412	#103	—	2	2	no	—
413	#102	—	2	2	no	—
414	#102	—	2	2	no	—
415	#102	—	2	2	no	—
416	#102	—	2	2	no	—
417	C₂²⋊C₈	—	2	1	no	—
418	C₂²⋊C₈	—	2	1	no	—
419	#97	—	2	1	no	—
420	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
421	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
422	C₁₉	#18934	1	1	yes	characteristic, direct product factor, Sylow
423	C₂⁴	—	2	4	no	—
424	#41	—	8	1	no	—
425	#41	—	8	2	no	—
426	#41	—	8	1	no	—
427	#41	—	8	2	no	—
428	#41	—	8	2	no	—
429	C₂×Q₈	—	2	1	no	—
430	C₂×Q₈	—	2	1	no	—
431	C₂×Q₈	—	2	1	no	—
432	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
433	C₂×D₄	—	2	4	no	—
434	C₂×D₄	—	2	4	no	—
435	C₂×D₄	—	2	4	no	—
436	C₂×D₄	—	2	2	no	—
437	C₂×D₄	—	2	2	no	—
438	C₂×D₄	—	2	2	no	—
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	—	2	1	no	—
442	C₂×D₄	—	2	1	no	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	—	2	1	no	—
445	C₂×D₄	—	2	1	no	—
446	C₂×D₄	—	2	1	no	—
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	—	4	1	no	—
449	C₂×D₄	—	8	2	no	—
450	C₂×D₄	—	8	2	no	—
451	C₂×D₄	—	8	2	no	—
452	C₂×D₄	—	8	2	no	—
453	C₂×D₄	—	8	4	no	—
454	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
455	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
456	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
457	C₂²×C₄	—	2	2	no	—
458	C₂²×C₄	—	2	2	no	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	4	1	no	—
461	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
462	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
463	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
464	SD₁₆	—	8	2	no	—
465	SD₁₆	—	8	2	no	—
466	D₈	—	8	2	no	—
467	D₈	—	8	2	no	—
468	D₈	—	8	2	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	2	2	no	—
472	C₂×C₈	—	2	2	no	—
473	C₂×C₈	—	8	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
481	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
482	C₂²⋊C₄	—	2	4	no	—
483	C₂²⋊C₄	—	2	4	no	—
484	C₂²⋊C₄	—	2	4	no	—
485	C₂²⋊C₄	—	2	2	no	—
486	C₂²⋊C₄	—	2	2	no	—
487	C₂²⋊C₄	—	2	2	no	—
488	C₂²⋊C₄	—	2	2	no	—
489	C₂²⋊C₄	—	2	2	no	—
490	C₂²⋊C₄	—	2	2	no	—
491	C₂²⋊C₄	—	4	1	no	—
492	C₂²⋊C₄	—	4	1	no	—
493	C₄²	—	2	4	no	—
494	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
495	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
496	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
497	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
498	C₂³	—	2	2	no	—
499	C₂³	—	2	2	no	—
500	C₂³	—	2	2	no	—
501	C₂³	—	4	1	no	—
502	C₂³	—	8	4	no	—
503	C₂³	—	8	4	no	—
504	C₂³	—	8	4	no	—
505	C₂³	C₁₉×#120	1	1	yes	characteristic
506	Q₈	—	4	2	no	—
507	Q₈	—	4	2	no	—
508	Q₈	—	8	1	no	—
509	Q₈	—	8	1	no	—
510	D₄	—	2	2	no	—
511	D₄	—	2	2	no	—
512	D₄	—	2	2	no	—
513	D₄	—	2	2	no	—
514	D₄	—	4	2	no	—
515	D₄	—	4	2	no	—
516	D₄	—	4	2	no	—
517	D₄	—	4	2	no	—
518	D₄	—	4	2	no	—
519	D₄	—	4	1	no	—
520	D₄	—	4	1	no	—
521	D₄	—	4	2	no	—
522	D₄	—	4	1	no	—
523	D₄	—	4	1	no	—
524	D₄	—	8	1	no	—
525	D₄	—	8	1	no	—
526	D₄	—	8	2	no	—
527	D₄	—	8	2	no	—
528	D₄	—	8	2	no	—
529	D₄	—	8	4	no	—
530	D₄	—	8	4	no	—
531	D₄	—	8	4	no	—
532	D₄	—	8	2	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	4	no	—
541	C₂×C₄	—	4	2	no	—
542	C₂×C₄	—	4	2	no	—
543	C₂×C₄	—	4	2	no	—
544	C₂×C₄	—	4	2	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	8	2	no	—
547	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
548	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
549	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
550	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
551	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
552	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
553	C₈	—	4	1	no	—
554	C₈	—	4	1	no	—
555	C₈	—	4	2	no	—
556	C₈	—	4	2	no	—
557	C₂²	—	2	1	no	—
558	C₂²	—	2	1	no	—
559	C₂²	—	2	1	no	—
560	C₂²	—	4	2	no	—
561	C₂²	—	4	2	no	—
562	C₂²	—	4	2	no	—
563	C₂²	—	4	2	no	—
564	C₂²	—	4	2	no	—
565	C₂²	—	4	2	no	—
566	C₂²	—	4	2	no	—
567	C₂²	—	4	2	no	—
568	C₂²	—	4	2	no	—
569	C₂²	—	8	1	no	—
570	C₂²	—	8	1	no	—
571	C₂²	—	8	1	no	—
572	C₂²	—	16	8	no	—
573	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
574	C₄	—	2	1	no	—
575	C₄	—	2	1	no	—
576	C₄	—	2	1	no	—
577	C₄	—	2	1	no	—
578	C₄	—	4	2	no	—
579	C₄	—	4	2	no	—
580	C₄	—	4	2	no	—
581	C₄	—	8	1	no	—
582	C₄	C₁₉×#576	1	2	yes	—
583	C₄	C₁₉×#576	1	1	yes	characteristic
584	C₄	C₁₉×#577	1	1	yes	characteristic
585	C₂	—	4	1	no	—
586	C₂	—	8	2	no	—
587	C₂	—	8	2	no	—
588	C₂	—	8	2	no	—
589	C₂	—	16	1	no	—
590	C₂	C₁₉×#3008	1	1	yes	characteristic
591	C₂	C₁₉×#3012	1	1	yes	characteristic
592	C₂	C₁₉×#3019	1	1	yes	characteristic

	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×#3549	C₂	semidirect
2. C₁₉×#3245	C₂	semidirect
3. C₁₉×#3214	C₂	semidirect
4. C₁₉×#3207	C₂	semidirect
5. C₁₉×#1646	C₂	semidirect
6. C₁₉×#1639	C₂	semidirect
7. C₁₉×#1624	C₂	semidirect
8. C₁₉×#1619	C₂	semidirect
9. C₁₉×#1551	C₂	semidirect
10. C₁₉×#1496	C₂	semidirect
11. C₁₉×#1480	C₂	semidirect
25. C₁₉×#532	C₂²	semidirect
28. C₁₉×#492	C₂²	semidirect
30. C₁₉×#487	C₂²	semidirect
33. C₁₉×#474	C₂²	semidirect
36. C₁₉×#461	C₂²	semidirect
38. C₁₉×#459	C₂²	semidirect
39. C₁₉×#459	C₂²	semidirect
42. C₁₉×#432	C₂²	semidirect
43. C₁₉×#431	C₂²	semidirect
44. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
45. C₁₉×#333	C₂²	semidirect
47. C₁₉×D₄⋊C₈	C₂²	semidirect
48. C₁₉×D₄⋊C₈	C₂²	semidirect
49. C₁₉×D₄⋊C₈	C₂²	semidirect
50. C₁₉×D₄⋊C₈	C₂²	semidirect
201. #18934	C₁₉	direct (N × H)
261. #3549	C₂×C₁₉	semidirect
262. #3245	C₂×C₁₉	semidirect
263. #3214	C₂×C₁₉	semidirect
264. #3207	C₂×C₁₉	semidirect
265. #1646	C₂×C₁₉	semidirect
266. #1639	C₂×C₁₉	semidirect
267. #1624	C₂×C₁₉	semidirect
268. #1619	C₂×C₁₉	semidirect
269. #1551	C₂×C₁₉	semidirect
270. #1496	C₂×C₁₉	semidirect
271. #1480	C₂×C₁₉	semidirect
313. #532	C₂²×C₁₉	semidirect
316. #492	C₂²×C₁₉	semidirect
318. #487	C₂²×C₁₉	semidirect
321. #474	C₂²×C₁₉	semidirect
324. #461	C₂²×C₁₉	semidirect
326. #459	C₂²×C₁₉	semidirect
327. #459	C₂²×C₁₉	semidirect
330. #432	C₂²×C₁₉	semidirect
331. #431	C₂²×C₁₉	semidirect
332. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
333. #333	C₂²×C₁₉	semidirect
335. D₄⋊C₈	C₂²×C₁₉	semidirect
336. D₄⋊C₈	C₂²×C₁₉	semidirect
337. D₄⋊C₈	C₂²×C₁₉	semidirect
338. D₄⋊C₈	C₂²×C₁₉	semidirect
422. C₁₉	#18934	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×#3549	2
C₁₉×#3245	2
C₁₉×#3214	2
C₁₉×#3207	2
C₁₉×#1646	2
C₁₉×#1639	2
C₁₉×#1624	2
C₁₉×#1619	2
C₁₉×#1551	2
C₁₉×#1496	2
C₁₉×#1480	2
#18934	19

Subgroups — C19×#18934 #18024893

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18934 #18024893