Subgroups — C₁₉×#19093 #18025052

Order 4864.

782 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3563	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3240	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3237	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3236	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1664	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1664	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1663	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1663	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1537	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1535	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1534	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#564	C₂²	1	2	yes	—
13	C₁₉×#563	C₂²	1	2	yes	—
14	C₁₉×#557	—	2	1	no	—
15	C₁₉×#554	—	2	1	no	—
16	C₁₉×#552	—	2	1	no	—
17	C₁₉×#552	—	2	2	no	—
18	C₁₉×#552	—	2	1	no	—
19	C₁₉×#544	—	2	1	no	—
20	C₁₉×#544	—	2	1	no	—
21	C₁₉×#541	—	2	1	no	—
22	C₁₉×#541	—	2	2	no	—
23	C₁₉×#539	—	2	1	no	—
24	C₁₉×#533	C₂²	1	1	yes	characteristic
25	C₁₉×#533	C₂²	1	1	yes	characteristic
26	C₁₉×#529	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
28	C₁₉×#501	C₂²	1	1	yes	characteristic
29	C₁₉×#501	C₂²	1	1	yes	characteristic
30	C₁₉×#501	C₂²	1	2	yes	—
31	C₁₉×#501	C₂²	1	2	yes	—
32	C₁₉×#491	C₂²	1	2	yes	—
33	C₁₉×#491	C₂²	1	2	yes	—
34	C₁₉×#489	C₂²	1	1	yes	characteristic
35	C₁₉×#489	C₂²	1	1	yes	characteristic
36	C₁₉×#485	—	2	1	no	—
37	C₁₉×#485	—	2	2	no	—
38	C₁₉×#484	—	2	1	no	—
39	C₁₉×#483	—	2	1	no	—
40	C₁₉×#482	—	2	1	no	—
41	C₁₉×#479	—	2	2	no	—
42	C₁₉×#479	—	2	1	no	—
43	C₁₉×#478	—	2	1	no	—
44	C₁₉×#477	—	2	1	no	—
45	C₁₉×#475	—	2	1	no	—
46	C₁₉×#432	C₂²	1	1	yes	characteristic
47	C₁₉×#432	C₂²	1	1	yes	characteristic
48	C₁₉×#432	C₂²	1	1	yes	characteristic
49	C₁₉×#330	C₂²	1	2	yes	—
50	C₁₉×#330	C₂²	1	2	yes	—
51	C₁₉×#330	C₂²	1	2	yes	—
52	C₁₉×#330	C₂²	1	2	yes	—
53	C₁₉×#330	C₂²	1	2	yes	—
54	C₁₉×#329	C₂²	1	2	yes	—
55	C₁₉×C₄⋊Q₈	—	2	2	no	—
56	C₁₉×C₄⋊Q₈	—	2	1	no	—
57	C₁₉×C₄⋊Q₈	—	2	2	no	—
58	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
59	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
60	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
61	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
62	C₁₉×#126	—	2	2	no	—
63	C₁₉×#126	—	2	2	no	—
64	C₁₉×#126	—	2	2	no	—
65	C₁₉×#126	—	2	2	no	—
66	C₁₉×#126	—	2	1	no	—
67	C₁₉×#125	—	2	2	no	—
68	C₁₉×#125	—	2	2	no	—
69	C₁₉×#125	—	2	1	no	—
70	C₁₉×#125	—	2	2	no	—
71	C₁₉×#125	—	2	2	no	—
72	C₁₉×#125	—	2	2	no	—
73	C₁₉×#125	—	2	2	no	—
74	C₁₉×#125	—	2	2	no	—
75	C₁₉×#125	—	2	2	no	—
76	C₁₉×#125	—	2	1	no	—
77	C₁₉×#125	—	2	1	no	—
78	C₁₉×#125	—	2	1	no	—
79	C₁₉×#125	D₄	1	2	yes	—
80	C₁₉×#125	C₂³	1	2	yes	—
81	C₁₉×#125	C₂³	1	2	yes	—
82	C₁₉×#125	C₂³	1	1	yes	characteristic
83	C₁₉×#124	C₂³	1	1	yes	characteristic
84	C₁₉×#123	—	2	2	no	—
85	C₁₉×#123	—	2	2	no	—
86	C₁₉×#123	—	2	1	no	—
87	C₁₉×C₂²⋊Q₈	—	2	2	no	—
88	C₁₉×C₂²⋊Q₈	—	2	1	no	—
89	C₁₉×C₂²⋊Q₈	—	2	1	no	—
90	C₁₉×C₂²⋊Q₈	—	2	2	no	—
91	C₁₉×C₂²⋊Q₈	—	2	1	no	—
92	C₁₉×C₂²⋊Q₈	—	2	1	no	—
93	C₁₉×C₂²⋊Q₈	—	2	2	no	—
94	C₁₉×C₂²⋊Q₈	—	2	2	no	—
95	C₁₉×C₂²⋊Q₈	—	2	1	no	—
96	C₁₉×C₂²⋊Q₈	—	2	1	no	—
97	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
98	C₁₉×#121	D₄	1	1	yes	characteristic
99	C₄×Q₈×C₁₉	—	2	1	no	—
100	C₄×Q₈×C₁₉	—	2	2	no	—
101	C₄×Q₈×C₁₉	—	2	1	no	—
102	C₄×Q₈×C₁₉	—	2	1	no	—
103	C₄×Q₈×C₁₉	—	2	1	no	—
104	C₄×Q₈×C₁₉	—	2	1	no	—
105	C₄×Q₈×C₁₉	—	2	1	no	—
106	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
107	C₄×D₄×C₁₉	—	2	2	no	—
108	C₄×D₄×C₁₉	—	2	1	no	—
109	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
110	C₁₉×#117	—	2	2	no	—
111	C₁₉×#117	—	2	1	no	—
112	C₁₉×#117	—	2	2	no	—
113	C₁₉×#117	—	2	1	no	—
114	C₁₉×#117	—	2	1	no	—
115	C₁₉×#117	D₄	1	2	yes	—
116	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
117	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
118	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
119	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
121	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
122	C₁₉×#107	—	2	2	no	—
123	C₁₉×#107	—	2	1	no	—
124	C₁₉×#107	—	2	1	no	—
125	C₁₉×#107	—	2	2	no	—
126	C₁₉×#106	—	2	2	no	—
127	C₁₉×#106	—	2	1	no	—
128	C₁₉×#106	—	2	1	no	—
129	C₁₉×#106	—	2	2	no	—
130	C₁₉×C₄⋊C₈	—	2	1	no	—
131	C₁₉×C₄⋊C₈	—	2	1	no	—
132	C₁₉×C₄⋊C₈	—	2	1	no	—
133	C₁₉×#103	—	2	1	no	—
134	C₁₉×#103	—	2	1	no	—
135	C₁₉×#103	—	2	2	no	—
136	C₁₉×#103	—	2	2	no	—
137	C₁₉×#103	—	2	2	no	—
138	C₁₉×#103	—	2	2	no	—
139	C₁₉×#102	—	2	1	no	—
140	C₁₉×#102	—	2	1	no	—
141	C₁₉×C₂²⋊C₈	—	2	1	no	—
142	C₁₉×C₂²⋊C₈	—	2	1	no	—
143	C₁₉×C₂²⋊C₈	—	2	1	no	—
144	C₁₉×#97	C₂³	1	1	yes	characteristic
145	C₁₉×#97	C₂³	1	1	yes	characteristic
146	C₁₉×#97	C₂³	1	2	yes	—
147	C₁₉×#97	C₂³	1	2	yes	—
148	C₂×Q₈×C₁₉	—	2	2	no	—
149	C₂×Q₈×C₁₉	—	2	1	no	—
150	C₂×Q₈×C₁₉	—	2	1	no	—
151	C₂×Q₈×C₁₉	—	2	1	no	—
152	C₂×Q₈×C₁₉	—	2	1	no	—
153	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₂×D₄×C₁₉	—	2	1	no	—
155	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₉	—	2	1	no	—
157	C₂²×C₄×C₁₉	—	2	2	no	—
158	C₂²×C₄×C₁₉	—	2	1	no	—
159	C₂²×C₄×C₁₉	—	2	1	no	—
160	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
163	C₂×C₈×C₁₉	—	2	1	no	—
164	C₂×C₈×C₁₉	—	2	1	no	—
165	C₂×C₈×C₁₉	—	2	2	no	—
166	C₂×C₈×C₁₉	—	2	2	no	—
167	C₄⋊C₄×C₁₉	—	2	2	no	—
168	C₄⋊C₄×C₁₉	—	2	2	no	—
169	C₄⋊C₄×C₁₉	—	2	2	no	—
170	C₄⋊C₄×C₁₉	—	2	2	no	—
171	C₄⋊C₄×C₁₉	—	2	2	no	—
172	C₄⋊C₄×C₁₉	—	2	2	no	—
173	C₄⋊C₄×C₁₉	—	2	2	no	—
174	C₄⋊C₄×C₁₉	—	2	2	no	—
175	C₄⋊C₄×C₁₉	—	2	1	no	—
176	C₄⋊C₄×C₁₉	—	2	1	no	—
177	C₄⋊C₄×C₁₉	—	2	2	no	—
178	C₄⋊C₄×C₁₉	—	2	2	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	2	no	—
184	C₄⋊C₄×C₁₉	—	2	2	no	—
185	C₄⋊C₄×C₁₉	—	2	1	no	—
186	C₄⋊C₄×C₁₉	—	2	1	no	—
187	C₄⋊C₄×C₁₉	—	2	2	no	—
188	C₄⋊C₄×C₁₉	—	2	2	no	—
189	C₄⋊C₄×C₁₉	—	2	1	no	—
190	C₄⋊C₄×C₁₉	—	2	1	no	—
191	C₄⋊C₄×C₁₉	—	2	1	no	—
192	C₄⋊C₄×C₁₉	—	2	1	no	—
193	C₄⋊C₄×C₁₉	—	4	1	no	—
194	C₄⋊C₄×C₁₉	—	4	1	no	—
195	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
196	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
197	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
198	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
199	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
200	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
201	C₂²⋊C₄×C₁₉	—	2	2	no	—
202	C₂²⋊C₄×C₁₉	—	2	2	no	—
203	C₂²⋊C₄×C₁₉	—	2	2	no	—
204	C₂²⋊C₄×C₁₉	—	2	1	no	—
205	C₂²⋊C₄×C₁₉	—	2	2	no	—
206	C₂²⋊C₄×C₁₉	—	2	1	no	—
207	C₂²⋊C₄×C₁₉	—	2	1	no	—
208	C₂²⋊C₄×C₁₉	—	2	1	no	—
209	C₂²⋊C₄×C₁₉	—	2	1	no	—
210	C₂²⋊C₄×C₁₉	—	4	1	no	—
211	C₄²×C₁₉	—	2	2	no	—
212	C₄²×C₁₉	—	2	2	no	—
213	C₄²×C₁₉	—	2	2	no	—
214	C₄²×C₁₉	—	2	2	no	—
215	C₄²×C₁₉	—	2	1	no	—
216	C₄²×C₁₉	—	4	1	no	—
217	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
218	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
219	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
220	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
221	#19093	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
222	C₂³×C₁₉	—	2	1	no	—
223	C₂³×C₁₉	#120	1	1	yes	characteristic
224	Q₈×C₁₉	—	4	1	no	—
225	Q₈×C₁₉	—	4	2	no	—
226	Q₈×C₁₉	—	4	2	no	—
227	Q₈×C₁₉	—	4	2	no	—
228	Q₈×C₁₉	—	8	1	no	—
229	Q₈×C₁₉	—	8	2	no	—
230	D₄×C₁₉	—	4	1	no	—
231	D₄×C₁₉	—	4	2	no	—
232	C₂×C₄×C₁₉	—	2	2	no	—
233	C₂×C₄×C₁₉	—	2	1	no	—
234	C₂×C₄×C₁₉	—	2	1	no	—
235	C₂×C₄×C₁₉	—	2	1	no	—
236	C₂×C₄×C₁₉	—	2	2	no	—
237	C₂×C₄×C₁₉	—	2	2	no	—
238	C₂×C₄×C₁₉	—	2	2	no	—
239	C₂×C₄×C₁₉	—	4	1	no	—
240	C₂×C₄×C₁₉	—	4	1	no	—
241	C₂×C₄×C₁₉	—	4	1	no	—
242	C₂×C₄×C₁₉	—	4	2	no	—
243	C₂×C₄×C₁₉	—	4	2	no	—
244	C₂×C₄×C₁₉	—	4	1	no	—
245	C₂×C₄×C₁₉	—	4	1	no	—
246	C₂×C₄×C₁₉	—	8	1	no	—
247	C₂×C₄×C₁₉	—	8	2	no	—
248	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
249	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
250	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
251	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
252	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
253	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
254	C₈×C₁₉	—	4	2	no	—
255	C₈×C₁₉	—	4	2	no	—
256	C₈×C₁₉	—	4	1	no	—
257	C₈×C₁₉	—	4	1	no	—
258	#3563	C₂×C₁₉	1	1	yes	characteristic
259	#3240	C₂×C₁₉	1	1	yes	characteristic
260	#3237	C₂×C₁₉	1	1	yes	characteristic, complemented
261	#3236	C₂×C₁₉	1	1	yes	characteristic, complemented
262	#1664	C₂×C₁₉	1	2	yes	complemented
263	#1664	C₂×C₁₉	1	2	yes	complemented
264	#1663	C₂×C₁₉	1	2	yes	complemented
265	#1663	C₂×C₁₉	1	2	yes	complemented
266	#1537	C₂×C₁₉	1	1	yes	characteristic, complemented
267	#1535	C₂×C₁₉	1	1	yes	characteristic
268	#1534	C₂×C₁₉	1	1	yes	characteristic, complemented
269	C₂²×C₁₉	—	2	1	no	—
270	C₂²×C₁₉	—	2	1	no	—
271	C₂²×C₁₉	—	2	1	no	—
272	C₂²×C₁₉	—	4	1	no	—
273	C₂²×C₁₉	—	4	1	no	—
274	C₂²×C₁₉	—	4	1	no	—
275	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
276	C₄×C₁₉	—	2	1	no	—
277	C₄×C₁₉	—	2	1	no	—
278	C₄×C₁₉	—	2	1	no	—
279	C₄×C₁₉	—	2	1	no	—
280	C₄×C₁₉	—	2	1	no	—
281	C₄×C₁₉	—	2	1	no	—
282	C₄×C₁₉	—	4	1	no	—
283	C₄×C₁₉	—	4	2	no	—
284	C₄×C₁₉	—	4	1	no	—
285	C₄×C₁₉	—	4	2	no	—
286	C₄×C₁₉	—	4	2	no	—
287	C₄×C₁₉	—	4	2	no	—
288	C₄×C₁₉	—	4	1	no	—
289	C₄×C₁₉	—	8	1	no	—
290	C₄×C₁₉	—	8	1	no	—
291	#564	C₂²×C₁₉	1	2	yes	—
292	#563	C₂²×C₁₉	1	2	yes	—
293	#557	—	2	1	no	—
294	#554	—	2	1	no	—
295	#552	—	2	1	no	—
296	#552	—	2	2	no	—
297	#552	—	2	1	no	—
298	#544	—	2	1	no	—
299	#544	—	2	1	no	—
300	#541	—	2	1	no	—
301	#541	—	2	2	no	—
302	#539	—	2	1	no	—
303	#533	C₂²×C₁₉	1	1	yes	characteristic
304	#533	C₂²×C₁₉	1	1	yes	characteristic
305	#529	C₂²×C₁₉	1	1	yes	characteristic
306	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
307	#501	C₂²×C₁₉	1	1	yes	characteristic
308	#501	C₂²×C₁₉	1	1	yes	characteristic
309	#501	C₂²×C₁₉	1	2	yes	—
310	#501	C₂²×C₁₉	1	2	yes	—
311	#491	C₂²×C₁₉	1	2	yes	—
312	#491	C₂²×C₁₉	1	2	yes	—
313	#489	C₂²×C₁₉	1	1	yes	characteristic
314	#489	C₂²×C₁₉	1	1	yes	characteristic
315	#485	—	2	1	no	—
316	#485	—	2	2	no	—
317	#484	—	2	1	no	—
318	#483	—	2	1	no	—
319	#482	—	2	1	no	—
320	#479	—	2	2	no	—
321	#479	—	2	1	no	—
322	#478	—	2	1	no	—
323	#477	—	2	1	no	—
324	#475	—	2	1	no	—
325	#432	C₂²×C₁₉	1	1	yes	characteristic
326	#432	C₂²×C₁₉	1	1	yes	characteristic
327	#432	C₂²×C₁₉	1	1	yes	characteristic
328	#330	C₂²×C₁₉	1	2	yes	—
329	#330	C₂²×C₁₉	1	2	yes	—
330	#330	C₂²×C₁₉	1	2	yes	—
331	#330	C₂²×C₁₉	1	2	yes	—
332	#330	C₂²×C₁₉	1	2	yes	—
333	#329	C₂²×C₁₉	1	2	yes	—
334	C₂×C₁₉	—	4	1	no	—
335	C₂×C₁₉	—	8	1	no	—
336	C₂×C₁₉	#3020	1	1	yes	characteristic
337	C₂×C₁₉	#3020	1	1	yes	characteristic
338	C₂×C₁₉	#3022	1	1	yes	characteristic
339	C₄⋊Q₈	—	2	2	no	—
340	C₄⋊Q₈	—	2	1	no	—
341	C₄⋊Q₈	—	2	2	no	—
342	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
343	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
344	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
345	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
346	#126	—	2	2	no	—
347	#126	—	2	2	no	—
348	#126	—	2	2	no	—
349	#126	—	2	2	no	—
350	#126	—	2	1	no	—
351	#125	—	2	2	no	—
352	#125	—	2	2	no	—
353	#125	—	2	1	no	—
354	#125	—	2	2	no	—
355	#125	—	2	2	no	—
356	#125	—	2	2	no	—
357	#125	—	2	2	no	—
358	#125	—	2	2	no	—
359	#125	—	2	2	no	—
360	#125	—	2	1	no	—
361	#125	—	2	1	no	—
362	#125	—	2	1	no	—
363	#125	D₄×C₁₉	1	2	yes	—
364	#125	C₂³×C₁₉	1	2	yes	—
365	#125	C₂³×C₁₉	1	1	yes	characteristic
366	#125	C₂³×C₁₉	1	2	yes	—
367	#124	C₂³×C₁₉	1	1	yes	characteristic
368	#123	—	2	2	no	—
369	#123	—	2	2	no	—
370	#123	—	2	1	no	—
371	C₂²⋊Q₈	—	2	2	no	—
372	C₂²⋊Q₈	—	2	1	no	—
373	C₂²⋊Q₈	—	2	1	no	—
374	C₂²⋊Q₈	—	2	2	no	—
375	C₂²⋊Q₈	—	2	1	no	—
376	C₂²⋊Q₈	—	2	1	no	—
377	C₂²⋊Q₈	—	2	2	no	—
378	C₂²⋊Q₈	—	2	2	no	—
379	C₂²⋊Q₈	—	2	1	no	—
380	C₂²⋊Q₈	—	2	1	no	—
381	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
382	#121	D₄×C₁₉	1	1	yes	characteristic
383	C₄×Q₈	—	2	1	no	—
384	C₄×Q₈	—	2	2	no	—
385	C₄×Q₈	—	2	1	no	—
386	C₄×Q₈	—	2	1	no	—
387	C₄×Q₈	—	2	1	no	—
388	C₄×Q₈	—	2	1	no	—
389	C₄×Q₈	—	2	1	no	—
390	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
391	C₄×D₄	—	2	2	no	—
392	C₄×D₄	—	2	1	no	—
393	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
394	#117	—	2	2	no	—
395	#117	—	2	1	no	—
396	#117	—	2	2	no	—
397	#117	—	2	1	no	—
398	#117	—	2	1	no	—
399	#117	D₄×C₁₉	1	2	yes	—
400	C₂×C₄⋊C₄	—	2	1	no	—
401	C₂×C₄⋊C₄	—	2	1	no	—
402	C₂×C₄⋊C₄	—	2	1	no	—
403	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
404	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
405	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
406	#107	—	2	2	no	—
407	#107	—	2	1	no	—
408	#107	—	2	1	no	—
409	#107	—	2	2	no	—
410	#106	—	2	2	no	—
411	#106	—	2	1	no	—
412	#106	—	2	1	no	—
413	#106	—	2	2	no	—
414	C₄⋊C₈	—	2	1	no	—
415	C₄⋊C₈	—	2	1	no	—
416	C₄⋊C₈	—	2	1	no	—
417	#103	—	2	1	no	—
418	#103	—	2	1	no	—
419	#103	—	2	2	no	—
420	#103	—	2	2	no	—
421	#103	—	2	2	no	—
422	#103	—	2	2	no	—
423	#102	—	2	1	no	—
424	#102	—	2	1	no	—
425	C₂²⋊C₈	—	2	1	no	—
426	C₂²⋊C₈	—	2	1	no	—
427	C₂²⋊C₈	—	2	1	no	—
428	#97	C₂³×C₁₉	1	2	yes	—
429	#97	C₂³×C₁₉	1	2	yes	—
430	#97	C₂³×C₁₉	1	1	yes	characteristic
431	#97	C₂³×C₁₉	1	1	yes	characteristic
432	C₁₉	#19093	1	1	yes	characteristic, direct product factor, Sylow
433	C₂×Q₈	—	2	2	no	—
434	C₂×Q₈	—	2	1	no	—
435	C₂×Q₈	—	2	1	no	—
436	C₂×Q₈	—	2	1	no	—
437	C₂×Q₈	—	2	1	no	—
438	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
446	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
447	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	2	no	—
451	C₂×C₈	—	2	2	no	—
452	C₄⋊C₄	—	2	2	no	—
453	C₄⋊C₄	—	2	2	no	—
454	C₄⋊C₄	—	2	2	no	—
455	C₄⋊C₄	—	2	2	no	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	2	2	no	—
458	C₄⋊C₄	—	2	2	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	2	no	—
463	C₄⋊C₄	—	2	2	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	2	no	—
469	C₄⋊C₄	—	2	2	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	2	no	—
473	C₄⋊C₄	—	2	2	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	—	4	1	no	—
479	C₄⋊C₄	—	4	1	no	—
480	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
481	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
482	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
483	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
484	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
485	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
486	C₂²⋊C₄	—	2	2	no	—
487	C₂²⋊C₄	—	2	2	no	—
488	C₂²⋊C₄	—	2	2	no	—
489	C₂²⋊C₄	—	2	1	no	—
490	C₂²⋊C₄	—	2	2	no	—
491	C₂²⋊C₄	—	2	1	no	—
492	C₂²⋊C₄	—	2	1	no	—
493	C₂²⋊C₄	—	2	1	no	—
494	C₂²⋊C₄	—	2	1	no	—
495	C₂²⋊C₄	—	4	1	no	—
496	C₄²	—	2	2	no	—
497	C₄²	—	2	2	no	—
498	C₄²	—	2	2	no	—
499	C₄²	—	2	2	no	—
500	C₄²	—	2	1	no	—
501	C₄²	—	4	1	no	—
502	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
503	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
504	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
505	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
506	C₂³	—	2	1	no	—
507	C₂³	C₁₉×#120	1	1	yes	characteristic
508	Q₈	—	4	1	no	—
509	Q₈	—	4	2	no	—
510	Q₈	—	4	2	no	—
511	Q₈	—	4	2	no	—
512	Q₈	—	8	1	no	—
513	Q₈	—	8	2	no	—
514	D₄	—	4	1	no	—
515	D₄	—	4	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	8	1	no	—
531	C₂×C₄	—	8	2	no	—
532	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
533	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
534	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
535	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
536	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
537	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
538	C₈	—	4	2	no	—
539	C₈	—	4	2	no	—
540	C₈	—	4	1	no	—
541	C₈	—	4	1	no	—
542	C₂²	—	2	1	no	—
543	C₂²	—	2	1	no	—
544	C₂²	—	2	1	no	—
545	C₂²	—	4	1	no	—
546	C₂²	—	4	1	no	—
547	C₂²	—	4	1	no	—
548	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
549	C₄	—	2	1	no	—
550	C₄	—	2	1	no	—
551	C₄	—	2	1	no	—
552	C₄	—	2	1	no	—
553	C₄	—	2	1	no	—
554	C₄	—	2	1	no	—
555	C₄	—	4	1	no	—
556	C₄	—	4	2	no	—
557	C₄	—	4	1	no	—
558	C₄	—	4	2	no	—
559	C₄	—	4	2	no	—
560	C₄	—	4	2	no	—
561	C₄	—	4	1	no	—
562	C₄	—	8	1	no	—
563	C₄	—	8	1	no	—
564	C₂	—	4	1	no	—
565	C₂	—	8	1	no	—
566	C₂	C₁₉×#3020	1	1	yes	characteristic
567	C₂	C₁₉×#3020	1	1	yes	characteristic
568	C₂	C₁₉×#3022	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#121	D₄
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
3. C₁₉×#3237	C₂	semidirect
4. C₁₉×#3236	C₂	semidirect
5. C₁₉×#1664	C₂	semidirect
6. C₁₉×#1664	C₂	semidirect
7. C₁₉×#1663	C₂	semidirect
8. C₁₉×#1663	C₂	semidirect
9. C₁₉×#1537	C₂	semidirect
11. C₁₉×#1534	C₂	semidirect
221. #19093	C₁₉	direct (N × H)
260. #3237	C₂×C₁₉	semidirect
261. #3236	C₂×C₁₉	semidirect
262. #1664	C₂×C₁₉	semidirect
263. #1664	C₂×C₁₉	semidirect
264. #1663	C₂×C₁₉	semidirect
265. #1663	C₂×C₁₉	semidirect
266. #1537	C₂×C₁₉	semidirect
268. #1534	C₂×C₁₉	semidirect
432. C₁₉	#19093	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×#3563	2
C₁₉×#3240	2
C₁₉×#3237	2
C₁₉×#3236	2
C₁₉×#1664	2
C₁₉×#1663	2
C₁₉×#1537	2
C₁₉×#1535	2
C₁₉×#1534	2
#19093	19

Subgroups — C19×#19093 #18025052

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19093 #18025052