Subgroups — C₁₉×#19311 #18025270

Order 4864.

578 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3185	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3113	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3078	C₂	1	1	yes	maximal, characteristic
4	Q₈×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1704	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1700	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1692	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1690	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1684	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1680	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1672	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1670	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1569	C₂	1	1	yes	maximal, characteristic
14	C₁₉×#1561	C₂	1	1	yes	maximal, characteristic
15	C₁₉×#1559	C₂	1	1	yes	maximal, characteristic
16	C₁₉×#533	C₂²	1	1	yes	characteristic
17	C₁₉×#533	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#498	C₂²	1	1	yes	characteristic
20	C₁₉×#494	C₂²	1	1	yes	characteristic
21	C₁₉×#487	C₂²	1	1	yes	characteristic
22	C₁₉×#487	C₂²	1	1	yes	characteristic
23	C₁₉×#483	—	2	1	no	—
24	C₁₉×#479	—	2	1	no	—
25	C₁₉×#479	—	2	1	no	—
26	C₁₉×#477	C₂²	1	1	yes	characteristic
27	C₁₉×#477	C₂²	1	1	yes	characteristic
28	C₁₉×#475	C₂²	1	1	yes	characteristic
29	C₁₉×#475	C₂²	1	1	yes	characteristic
30	C₁₉×#475	C₂²	1	1	yes	characteristic
31	C₁₉×#475	C₂²	1	1	yes	characteristic
32	C₁₉×#470	—	2	1	no	—
33	C₁₉×#470	—	2	1	no	—
34	C₁₉×#462	C₂²	1	1	yes	characteristic
35	C₁₉×#462	C₂²	1	1	yes	characteristic
36	C₁₉×#451	—	2	1	no	—
37	C₁₉×#446	—	2	1	no	—
38	C₁₉×#446	—	2	1	no	—
39	C₁₉×#446	C₂²	1	1	yes	characteristic
40	C₁₉×#446	C₂²	1	1	yes	characteristic
41	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
42	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
43	C₁₉×#441	—	2	1	no	—
44	C₁₉×#441	—	2	1	no	—
45	C₁₉×#441	—	2	1	no	—
46	C₁₉×#441	—	2	1	no	—
47	C₁₉×#432	C₂²	1	1	yes	characteristic
48	C₁₉×#428	—	2	1	no	—
49	C₁₉×#423	—	2	1	no	—
50	C₁₉×#423	C₂²	1	1	yes	characteristic
51	C₁₉×#423	C₂²	1	1	yes	characteristic
52	C₁₉×#419	—	2	1	no	—
53	C₄×M₁₆×C₁₉	—	2	1	no	—
54	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
55	C₁₉×#335	C₂²	1	1	yes	characteristic
56	C₁₉×#335	C₂²	1	1	yes	characteristic
57	C₁₉×#334	C₂²	1	1	yes	characteristic
58	C₁₉×#334	C₂²	1	1	yes	characteristic
59	C₁₉×#333	C₂²	1	1	yes	characteristic
60	C₁₉×#333	C₂²	1	1	yes	characteristic
61	C₁₉×#332	C₂²	1	1	yes	characteristic
62	C₁₉×#332	C₂²	1	1	yes	characteristic
63	C₁₉×#332	C₂²	1	1	yes	characteristic
64	C₁₉×#332	C₂²	1	1	yes	characteristic
65	C₁₉×#332	C₂²	1	1	yes	characteristic
66	C₁₉×#332	C₂²	1	1	yes	characteristic
67	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
68	C₂×Q₁₆×C₁₉	—	2	1	no	—
69	C₂×Q₁₆×C₁₉	—	2	1	no	—
70	C₂×Q₁₆×C₁₉	—	2	1	no	—
71	C₂×Q₁₆×C₁₉	—	2	1	no	—
72	C₂×M₁₆×C₁₉	—	2	1	no	—
73	C₂×M₁₆×C₁₉	—	2	1	no	—
74	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
75	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
76	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
77	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
78	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
79	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
80	C₁₉×#125	—	2	1	no	—
81	C₁₉×#125	—	2	1	no	—
82	C₁₉×C₂²⋊Q₈	—	2	1	no	—
83	C₁₉×C₂²⋊Q₈	—	2	1	no	—
84	C₁₉×C₂²⋊Q₈	—	2	1	no	—
85	C₁₉×C₂²⋊Q₈	—	2	1	no	—
86	C₄×Q₈×C₁₉	—	2	1	no	—
87	C₄×Q₈×C₁₉	—	2	1	no	—
88	C₄×Q₈×C₁₉	—	2	1	no	—
89	C₄×Q₈×C₁₉	—	2	1	no	—
90	C₄×Q₈×C₁₉	—	2	1	no	—
91	C₄×Q₈×C₁₉	—	2	1	no	—
92	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
93	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
94	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
95	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
96	C₁₉×#117	—	2	1	no	—
97	C₁₉×#117	—	2	1	no	—
98	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
99	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
100	C₂×C₄²×C₁₉	—	2	1	no	—
101	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
102	C₁₉×#107	—	2	1	no	—
103	C₁₉×#107	—	2	1	no	—
104	C₁₉×#106	—	2	1	no	—
105	C₁₉×#106	—	2	1	no	—
106	C₁₉×#106	—	2	1	no	—
107	C₁₉×#106	—	2	1	no	—
108	C₁₉×#106	—	2	1	no	—
109	C₁₉×#106	—	2	1	no	—
110	C₁₉×C₄⋊C₈	—	2	1	no	—
111	C₁₉×C₄⋊C₈	—	2	1	no	—
112	C₁₉×C₄⋊C₈	—	2	1	no	—
113	C₁₉×C₄⋊C₈	—	2	1	no	—
114	C₁₉×C₄⋊C₈	—	2	1	no	—
115	C₁₉×C₄⋊C₈	—	2	1	no	—
116	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
117	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
118	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
119	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
120	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
121	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
122	C₁₉×#103	—	2	1	no	—
123	C₁₉×#103	—	2	1	no	—
124	C₁₉×#103	—	2	1	no	—
125	C₁₉×#103	—	2	1	no	—
126	C₁₉×#103	—	2	1	no	—
127	C₁₉×#103	—	2	1	no	—
128	C₁₉×#103	—	2	1	no	—
129	C₁₉×#103	—	2	1	no	—
130	C₁₉×#103	—	2	1	no	—
131	C₁₉×#103	—	2	1	no	—
132	C₁₉×#103	—	2	1	no	—
133	C₁₉×#103	—	2	1	no	—
134	C₁₉×C₂²⋊C₈	—	2	1	no	—
135	C₁₉×#97	—	2	1	no	—
136	C₁₉×#97	—	2	1	no	—
137	C₁₉×#97	—	2	1	no	—
138	C₁₉×#97	D₄	1	1	yes	characteristic
139	C₁₉×#97	D₄	1	1	yes	characteristic
140	C₄×C₈×C₁₉	—	2	1	no	—
141	C₄×C₈×C₁₉	—	2	1	no	—
142	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
144	C₂×Q₈×C₁₉	—	2	1	no	—
145	C₂×Q₈×C₁₉	—	2	2	no	—
146	C₂×Q₈×C₁₉	—	2	1	no	—
147	C₂×Q₈×C₁₉	—	2	1	no	—
148	C₂×Q₈×C₁₉	—	2	1	no	—
149	C₂×Q₈×C₁₉	—	2	1	no	—
150	C₂×Q₈×C₁₉	—	4	1	no	—
151	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₉	—	2	1	no	—
154	C₂²×C₄×C₁₉	—	2	1	no	—
155	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
158	Q₁₆×C₁₉	—	4	2	no	—
159	Q₁₆×C₁₉	—	4	2	no	—
160	Q₁₆×C₁₉	—	4	2	no	—
161	Q₁₆×C₁₉	—	4	2	no	—
162	M₁₆×C₁₉	—	2	2	no	—
163	M₁₆×C₁₉	—	4	1	no	—
164	M₁₆×C₁₉	—	4	2	no	—
165	M₁₆×C₁₉	—	4	2	no	—
166	C₂×C₈×C₁₉	—	2	1	no	—
167	C₂×C₈×C₁₉	—	2	1	no	—
168	C₂×C₈×C₁₉	—	2	1	no	—
169	C₂×C₈×C₁₉	—	2	1	no	—
170	C₂×C₈×C₁₉	—	2	1	no	—
171	C₂×C₈×C₁₉	—	2	1	no	—
172	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
173	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
174	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
175	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
176	C₄⋊C₄×C₁₉	—	2	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	—	2	1	no	—
184	C₄⋊C₄×C₁₉	—	2	1	no	—
185	C₄⋊C₄×C₁₉	—	2	1	no	—
186	C₄⋊C₄×C₁₉	—	2	1	no	—
187	C₄⋊C₄×C₁₉	—	2	1	no	—
188	C₄⋊C₄×C₁₉	—	2	1	no	—
189	C₄⋊C₄×C₁₉	—	4	1	no	—
190	C₄⋊C₄×C₁₉	—	4	1	no	—
191	C₄⋊C₄×C₁₉	—	4	1	no	—
192	C₄⋊C₄×C₁₉	—	4	1	no	—
193	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
194	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
195	C₂²⋊C₄×C₁₉	—	4	1	no	—
196	C₂²⋊C₄×C₁₉	—	4	1	no	—
197	C₄²×C₁₉	—	2	1	no	—
198	C₄²×C₁₉	—	2	1	no	—
199	C₄²×C₁₉	—	2	1	no	—
200	C₄²×C₁₉	—	2	1	no	—
201	C₄²×C₁₉	—	4	1	no	—
202	C₄²×C₁₉	—	4	1	no	—
203	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
204	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
205	C₄²×C₁₉	#41	1	1	yes	characteristic
206	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
207	#19311	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
208	C₂³×C₁₉	#121	1	1	yes	characteristic
209	Q₈×C₁₉	—	2	1	no	—
210	Q₈×C₁₉	—	2	1	no	—
211	Q₈×C₁₉	—	2	1	no	—
212	Q₈×C₁₉	—	4	2	no	—
213	Q₈×C₁₉	—	4	1	no	—
214	Q₈×C₁₉	—	4	1	no	—
215	Q₈×C₁₉	—	4	1	no	—
216	Q₈×C₁₉	—	4	1	no	—
217	Q₈×C₁₉	—	4	1	no	—
218	Q₈×C₁₉	—	4	1	no	—
219	Q₈×C₁₉	—	8	1	no	—
220	Q₈×C₁₉	#137	1	2	yes	—
221	C₂×C₄×C₁₉	—	2	1	no	—
222	C₂×C₄×C₁₉	—	2	1	no	—
223	C₂×C₄×C₁₉	—	2	1	no	—
224	C₂×C₄×C₁₉	—	2	1	no	—
225	C₂×C₄×C₁₉	—	2	1	no	—
226	C₂×C₄×C₁₉	—	2	1	no	—
227	C₂×C₄×C₁₉	—	2	1	no	—
228	C₂×C₄×C₁₉	—	2	1	no	—
229	C₂×C₄×C₁₉	—	4	1	no	—
230	C₂×C₄×C₁₉	—	4	2	no	—
231	C₂×C₄×C₁₉	—	4	1	no	—
232	C₂×C₄×C₁₉	—	4	1	no	—
233	C₂×C₄×C₁₉	—	4	1	no	—
234	C₂×C₄×C₁₉	—	4	1	no	—
235	C₂×C₄×C₁₉	—	8	1	no	—
236	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
237	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
238	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
239	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
240	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
242	C₈×C₁₉	—	2	1	no	—
243	C₈×C₁₉	—	2	1	no	—
244	C₈×C₁₉	—	2	1	no	—
245	C₈×C₁₉	—	4	1	no	—
246	C₈×C₁₉	—	4	1	no	—
247	C₈×C₁₉	—	4	1	no	—
248	C₈×C₁₉	—	4	1	no	—
249	C₈×C₁₉	—	4	1	no	—
250	C₈×C₁₉	—	4	1	no	—
251	C₈×C₁₉	#137	1	2	yes	—
252	#3185	C₂×C₁₉	1	1	yes	characteristic
253	#3113	C₂×C₁₉	1	1	yes	characteristic
254	#3078	C₂×C₁₉	1	1	yes	characteristic
255	Q₈×M₁₆	C₂×C₁₉	1	1	yes	characteristic
256	#1704	C₂×C₁₉	1	1	yes	characteristic, complemented
257	#1700	C₂×C₁₉	1	1	yes	characteristic, complemented
258	#1692	C₂×C₁₉	1	1	yes	characteristic, complemented
259	#1690	C₂×C₁₉	1	1	yes	characteristic, complemented
260	#1684	C₂×C₁₉	1	1	yes	characteristic, complemented
261	#1680	C₂×C₁₉	1	1	yes	characteristic, complemented
262	#1672	C₂×C₁₉	1	1	yes	characteristic, complemented
263	#1670	C₂×C₁₉	1	1	yes	characteristic, complemented
264	#1569	C₂×C₁₉	1	1	yes	characteristic
265	#1561	C₂×C₁₉	1	1	yes	characteristic
266	#1559	C₂×C₁₉	1	1	yes	characteristic
267	C₂²×C₁₉	—	2	1	no	—
268	C₂²×C₁₉	—	2	1	no	—
269	C₂²×C₁₉	—	2	1	no	—
270	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
271	C₄×C₁₉	—	2	1	no	—
272	C₄×C₁₉	—	2	1	no	—
273	C₄×C₁₉	—	2	2	no	—
274	C₄×C₁₉	—	2	1	no	—
275	C₄×C₁₉	—	2	1	no	—
276	C₄×C₁₉	—	4	1	no	—
277	C₄×C₁₉	—	4	1	no	—
278	C₄×C₁₉	—	4	1	no	—
279	C₄×C₁₉	—	8	1	no	—
280	C₄×C₁₉	—	8	1	no	—
281	C₄×C₁₉	—	8	1	no	—
282	C₄×C₁₉	—	8	1	no	—
283	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
284	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
285	C₄×C₁₉	#575	1	1	yes	characteristic
286	C₄×C₁₉	#575	1	1	yes	characteristic
287	#533	C₂²×C₁₉	1	1	yes	characteristic
288	#533	C₂²×C₁₉	1	1	yes	characteristic
289	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
290	#498	C₂²×C₁₉	1	1	yes	characteristic
291	#494	C₂²×C₁₉	1	1	yes	characteristic
292	#487	C₂²×C₁₉	1	1	yes	characteristic
293	#487	C₂²×C₁₉	1	1	yes	characteristic
294	#483	—	2	1	no	—
295	#479	—	2	1	no	—
296	#479	—	2	1	no	—
297	#477	C₂²×C₁₉	1	1	yes	characteristic
298	#477	C₂²×C₁₉	1	1	yes	characteristic
299	#475	C₂²×C₁₉	1	1	yes	characteristic
300	#475	C₂²×C₁₉	1	1	yes	characteristic
301	#475	C₂²×C₁₉	1	1	yes	characteristic
302	#475	C₂²×C₁₉	1	1	yes	characteristic
303	#470	—	2	1	no	—
304	#470	—	2	1	no	—
305	#462	C₂²×C₁₉	1	1	yes	characteristic
306	#462	C₂²×C₁₉	1	1	yes	characteristic
307	#451	—	2	1	no	—
308	#446	—	2	1	no	—
309	#446	—	2	1	no	—
310	#446	C₂²×C₁₉	1	1	yes	characteristic
311	#446	C₂²×C₁₉	1	1	yes	characteristic
312	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
313	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
314	#441	—	2	1	no	—
315	#441	—	2	1	no	—
316	#441	—	2	1	no	—
317	#441	—	2	1	no	—
318	#432	C₂²×C₁₉	1	1	yes	characteristic
319	#428	—	2	1	no	—
320	#423	—	2	1	no	—
321	#423	C₂²×C₁₉	1	1	yes	characteristic
322	#423	C₂²×C₁₉	1	1	yes	characteristic
323	#419	—	2	1	no	—
324	C₄×M₁₆	—	2	1	no	—
325	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
326	#335	C₂²×C₁₉	1	1	yes	characteristic
327	#335	C₂²×C₁₉	1	1	yes	characteristic
328	#334	C₂²×C₁₉	1	1	yes	characteristic
329	#334	C₂²×C₁₉	1	1	yes	characteristic
330	#333	C₂²×C₁₉	1	1	yes	characteristic
331	#333	C₂²×C₁₉	1	1	yes	characteristic
332	#332	C₂²×C₁₉	1	1	yes	characteristic
333	#332	C₂²×C₁₉	1	1	yes	characteristic
334	#332	C₂²×C₁₉	1	1	yes	characteristic
335	#332	C₂²×C₁₉	1	1	yes	characteristic
336	#332	C₂²×C₁₉	1	1	yes	characteristic
337	#332	C₂²×C₁₉	1	1	yes	characteristic
338	C₂×C₁₉	—	4	1	no	—
339	C₂×C₁₉	#3037	1	1	yes	characteristic
340	C₂×C₁₉	#3056	1	1	yes	characteristic
341	C₂×C₁₉	#3069	1	1	yes	characteristic
342	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
343	C₂×Q₁₆	—	2	1	no	—
344	C₂×Q₁₆	—	2	1	no	—
345	C₂×Q₁₆	—	2	1	no	—
346	C₂×Q₁₆	—	2	1	no	—
347	C₂×M₁₆	—	2	1	no	—
348	C₂×M₁₆	—	2	1	no	—
349	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
350	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
351	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
352	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
353	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
354	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
355	#125	—	2	1	no	—
356	#125	—	2	1	no	—
357	C₂²⋊Q₈	—	2	1	no	—
358	C₂²⋊Q₈	—	2	1	no	—
359	C₂²⋊Q₈	—	2	1	no	—
360	C₂²⋊Q₈	—	2	1	no	—
361	C₄×Q₈	—	2	1	no	—
362	C₄×Q₈	—	2	1	no	—
363	C₄×Q₈	—	2	1	no	—
364	C₄×Q₈	—	2	1	no	—
365	C₄×Q₈	—	2	1	no	—
366	C₄×Q₈	—	2	1	no	—
367	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
368	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
369	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
370	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
371	#117	—	2	1	no	—
372	#117	—	2	1	no	—
373	C₂×C₄⋊C₄	—	2	1	no	—
374	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
375	C₂×C₄²	—	2	1	no	—
376	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
377	#107	—	2	1	no	—
378	#107	—	2	1	no	—
379	#106	—	2	1	no	—
380	#106	—	2	1	no	—
381	#106	—	2	1	no	—
382	#106	—	2	1	no	—
383	#106	—	2	1	no	—
384	#106	—	2	1	no	—
385	C₄⋊C₈	—	2	1	no	—
386	C₄⋊C₈	—	2	1	no	—
387	C₄⋊C₈	—	2	1	no	—
388	C₄⋊C₈	—	2	1	no	—
389	C₄⋊C₈	—	2	1	no	—
390	C₄⋊C₈	—	2	1	no	—
391	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
392	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
393	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
394	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
395	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
396	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
397	#103	—	2	1	no	—
398	#103	—	2	1	no	—
399	#103	—	2	1	no	—
400	#103	—	2	1	no	—
401	#103	—	2	1	no	—
402	#103	—	2	1	no	—
403	#103	—	2	1	no	—
404	#103	—	2	1	no	—
405	#103	—	2	1	no	—
406	#103	—	2	1	no	—
407	#103	—	2	1	no	—
408	#103	—	2	1	no	—
409	C₂²⋊C₈	—	2	1	no	—
410	#97	—	2	1	no	—
411	#97	—	2	1	no	—
412	#97	—	2	1	no	—
413	#97	D₄×C₁₉	1	1	yes	characteristic
414	#97	D₄×C₁₉	1	1	yes	characteristic
415	C₄×C₈	—	2	1	no	—
416	C₄×C₈	—	2	1	no	—
417	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
418	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
419	C₁₉	#19311	1	1	yes	characteristic, direct product factor, Sylow
420	C₂×Q₈	—	2	1	no	—
421	C₂×Q₈	—	2	2	no	—
422	C₂×Q₈	—	2	1	no	—
423	C₂×Q₈	—	2	1	no	—
424	C₂×Q₈	—	2	1	no	—
425	C₂×Q₈	—	2	1	no	—
426	C₂×Q₈	—	4	1	no	—
427	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
428	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
432	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
433	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
434	Q₁₆	—	4	2	no	—
435	Q₁₆	—	4	2	no	—
436	Q₁₆	—	4	2	no	—
437	Q₁₆	—	4	2	no	—
438	M₁₆	—	2	2	no	—
439	M₁₆	—	4	1	no	—
440	M₁₆	—	4	2	no	—
441	M₁₆	—	4	2	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
449	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
450	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
451	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	4	1	no	—
466	C₄⋊C₄	—	4	1	no	—
467	C₄⋊C₄	—	4	1	no	—
468	C₄⋊C₄	—	4	1	no	—
469	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
470	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
471	C₂²⋊C₄	—	4	1	no	—
472	C₂²⋊C₄	—	4	1	no	—
473	C₄²	—	2	1	no	—
474	C₄²	—	2	1	no	—
475	C₄²	—	2	1	no	—
476	C₄²	—	2	1	no	—
477	C₄²	—	4	1	no	—
478	C₄²	—	4	1	no	—
479	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
480	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
481	C₄²	#41×C₁₉	1	1	yes	characteristic
482	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
483	C₂³	C₁₉×#121	1	1	yes	characteristic
484	Q₈	—	2	1	no	—
485	Q₈	—	2	1	no	—
486	Q₈	—	2	1	no	—
487	Q₈	—	4	2	no	—
488	Q₈	—	4	1	no	—
489	Q₈	—	4	1	no	—
490	Q₈	—	4	1	no	—
491	Q₈	—	4	1	no	—
492	Q₈	—	4	1	no	—
493	Q₈	—	4	1	no	—
494	Q₈	—	8	1	no	—
495	Q₈	C₁₉×#137	1	2	yes	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	8	1	no	—
511	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
512	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
513	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
514	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
515	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
516	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
517	C₈	—	2	1	no	—
518	C₈	—	2	1	no	—
519	C₈	—	2	1	no	—
520	C₈	—	4	1	no	—
521	C₈	—	4	1	no	—
522	C₈	—	4	1	no	—
523	C₈	—	4	1	no	—
524	C₈	—	4	1	no	—
525	C₈	—	4	1	no	—
526	C₈	C₁₉×#137	1	2	yes	—
527	C₂²	—	2	1	no	—
528	C₂²	—	2	1	no	—
529	C₂²	—	2	1	no	—
530	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
531	C₄	—	2	1	no	—
532	C₄	—	2	1	no	—
533	C₄	—	2	2	no	—
534	C₄	—	2	1	no	—
535	C₄	—	2	1	no	—
536	C₄	—	4	1	no	—
537	C₄	—	4	1	no	—
538	C₄	—	4	1	no	—
539	C₄	—	8	1	no	—
540	C₄	—	8	1	no	—
541	C₄	—	8	1	no	—
542	C₄	—	8	1	no	—
543	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
544	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
545	C₄	C₁₉×#575	1	1	yes	characteristic
546	C₄	C₁₉×#575	1	1	yes	characteristic
547	C₂	—	4	1	no	—
548	C₂	C₁₉×#3037	1	1	yes	characteristic
549	C₂	C₁₉×#3056	1	1	yes	characteristic
550	C₂	C₁₉×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₂³×C₁₉	#121
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
5. C₁₉×#1704	C₂	semidirect
6. C₁₉×#1700	C₂	semidirect
7. C₁₉×#1692	C₂	semidirect
8. C₁₉×#1690	C₂	semidirect
9. C₁₉×#1684	C₂	semidirect
10. C₁₉×#1680	C₂	semidirect
11. C₁₉×#1672	C₂	semidirect
12. C₁₉×#1670	C₂	semidirect
207. #19311	C₁₉	direct (N × H)
256. #1704	C₂×C₁₉	semidirect
257. #1700	C₂×C₁₉	semidirect
258. #1692	C₂×C₁₉	semidirect
259. #1690	C₂×C₁₉	semidirect
260. #1684	C₂×C₁₉	semidirect
261. #1680	C₂×C₁₉	semidirect
262. #1672	C₂×C₁₉	semidirect
263. #1670	C₂×C₁₉	semidirect
419. C₁₉	#19311	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×#3185	2
C₁₉×#3113	2
C₁₉×#3078	2
Q₈×M₁₆×C₁₉	2
C₁₉×#1704	2
C₁₉×#1700	2
C₁₉×#1692	2
C₁₉×#1690	2
C₁₉×#1684	2
C₁₉×#1680	2
C₁₉×#1672	2
C₁₉×#1670	2
C₁₉×#1569	2
C₁₉×#1561	2
C₁₉×#1559	2
#19311	19

Subgroups — C19×#19311 #18025270

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19311 #18025270