Subgroups — C₁₉×#19375 #18025334

Order 4864.

554 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3255	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3237	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3185	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2962	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×#1552	C₂	1	1	yes	maximal, characteristic
15	C₁₉×#1550	C₂	1	1	yes	maximal, characteristic
16	C₁₉×#533	C₂²	1	1	yes	characteristic
17	C₁₉×#533	C₂²	1	1	yes	characteristic
18	C₁₉×#533	C₂²	1	1	yes	characteristic
19	C₁₉×#501	—	2	1	no	—
20	C₁₉×#498	C₂²	1	1	yes	characteristic
21	C₁₉×#494	C₂²	1	1	yes	characteristic
22	C₁₉×#491	—	2	1	no	—
23	C₁₉×#487	C₂²	1	1	yes	characteristic
24	C₁₉×#487	C₂²	1	1	yes	characteristic
25	C₁₉×#485	—	2	1	no	—
26	C₁₉×#485	—	2	1	no	—
27	C₁₉×#477	C₂²	1	1	yes	characteristic
28	C₁₉×#477	C₂²	1	1	yes	characteristic
29	C₁₉×#475	—	2	1	no	—
30	C₁₉×#475	C₂²	1	1	yes	characteristic
31	C₁₉×#475	C₂²	1	1	yes	characteristic
32	C₁₉×#475	C₂²	1	1	yes	characteristic
33	C₁₉×#475	C₂²	1	1	yes	characteristic
34	C₁₉×#470	—	2	1	no	—
35	C₁₉×#470	—	2	1	no	—
36	C₁₉×#470	—	2	1	no	—
37	C₁₉×#470	—	2	1	no	—
38	C₁₉×#462	—	2	1	no	—
39	C₁₉×#462	C₂²	1	1	yes	characteristic
40	C₁₉×#462	C₂²	1	1	yes	characteristic
41	C₁₉×#446	—	2	1	no	—
42	C₁₉×#446	—	2	1	no	—
43	C₁₉×#446	C₂²	1	1	yes	characteristic
44	C₁₉×#446	C₂²	1	1	yes	characteristic
45	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
46	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
47	C₁₉×#441	—	2	1	no	—
48	C₁₉×#441	—	2	1	no	—
49	C₁₉×#432	C₂²	1	1	yes	characteristic
50	C₁₉×#424	—	2	1	no	—
51	C₁₉×#423	C₂²	1	1	yes	characteristic
52	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
53	C₁₉×#405	—	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	C₂×Q₁₆×C₁₉	—	2	1	no	—
68	C₂×Q₁₆×C₁₉	—	2	1	no	—
69	C₂×Q₁₆×C₁₉	—	2	1	no	—
70	C₂×Q₁₆×C₁₉	—	2	1	no	—
71	C₂×M₁₆×C₁₉	—	2	1	no	—
72	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
73	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
74	C₂²×C₈×C₁₉	—	2	1	no	—
75	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
76	C₁₉×C₄⋊Q₈	D₄	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×C₄⋊Q₈	C₂³	1	1	yes	characteristic
81	C₁₉×#125	—	2	1	no	—
82	C₁₉×#125	—	2	1	no	—
83	C₁₉×#125	—	2	1	no	—
84	C₁₉×C₂²⋊Q₈	—	2	1	no	—
85	C₁₉×C₂²⋊Q₈	—	2	1	no	—
86	C₁₉×C₂²⋊Q₈	—	2	1	no	—
87	C₁₉×C₂²⋊Q₈	—	2	1	no	—
88	C₁₉×C₂²⋊Q₈	—	2	1	no	—
89	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
90	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
91	C₄×Q₈×C₁₉	—	2	1	no	—
92	C₄×Q₈×C₁₉	—	2	1	no	—
93	C₄×Q₈×C₁₉	—	2	1	no	—
94	C₄×Q₈×C₁₉	—	2	1	no	—
95	C₄×Q₈×C₁₉	—	2	1	no	—
96	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
97	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
98	C₁₉×#117	—	2	1	no	—
99	C₁₉×#117	—	2	1	no	—
100	C₁₉×#117	—	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	1	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	C₂×D₄	1	1	yes	characteristic
150	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
154	Q₁₆×C₁₉	—	4	2	no	—
155	Q₁₆×C₁₉	—	4	2	no	—
156	Q₁₆×C₁₉	—	8	1	no	—
157	Q₁₆×C₁₉	—	8	1	no	—
158	M₁₆×C₁₉	—	2	2	no	—
159	M₁₆×C₁₉	—	4	1	no	—
160	M₁₆×C₁₉	—	8	1	no	—
161	C₂×C₈×C₁₉	—	2	1	no	—
162	C₂×C₈×C₁₉	—	2	1	no	—
163	C₂×C₈×C₁₉	—	2	1	no	—
164	C₂×C₈×C₁₉	—	2	1	no	—
165	C₂×C₈×C₁₉	—	2	1	no	—
166	C₂×C₈×C₁₉	—	2	1	no	—
167	C₂×C₈×C₁₉	—	4	2	no	—
168	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
169	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
170	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
171	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
172	C₄⋊C₄×C₁₉	—	2	1	no	—
173	C₄⋊C₄×C₁₉	—	2	1	no	—
174	C₄⋊C₄×C₁₉	—	2	1	no	—
175	C₄⋊C₄×C₁₉	—	2	1	no	—
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	—	4	1	no	—
188	C₄⋊C₄×C₁₉	—	4	1	no	—
189	C₄⋊C₄×C₁₉	—	4	1	no	—
190	C₄⋊C₄×C₁₉	—	4	1	no	—
191	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
192	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
193	C₂²⋊C₄×C₁₉	—	2	1	no	—
194	C₂²⋊C₄×C₁₉	—	2	1	no	—
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	—	4	1	no	—
200	C₄²×C₁₉	—	4	1	no	—
201	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
202	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
203	C₄²×C₁₉	#41	1	1	yes	characteristic
204	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
205	#19375	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
206	C₂³×C₁₉	#121	1	1	yes	characteristic
207	Q₈×C₁₉	—	2	1	no	—
208	Q₈×C₁₉	—	2	1	no	—
209	Q₈×C₁₉	—	2	1	no	—
210	Q₈×C₁₉	—	2	1	no	—
211	Q₈×C₁₉	—	4	1	no	—
212	Q₈×C₁₉	—	4	1	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	—	8	1	no	—
218	Q₈×C₁₉	—	8	1	no	—
219	C₂×C₄×C₁₉	—	2	1	no	—
220	C₂×C₄×C₁₉	—	2	1	no	—
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	—	4	1	no	—
228	C₂×C₄×C₁₉	—	4	1	no	—
229	C₂×C₄×C₁₉	—	4	1	no	—
230	C₂×C₄×C₁₉	—	4	1	no	—
231	C₂×C₄×C₁₉	—	4	1	no	—
232	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
233	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
234	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
235	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
238	C₈×C₁₉	—	2	1	no	—
239	C₈×C₁₉	—	2	1	no	—
240	C₈×C₁₉	—	2	1	no	—
241	C₈×C₁₉	—	4	1	no	—
242	C₈×C₁₉	—	4	1	no	—
243	C₈×C₁₉	—	4	1	no	—
244	C₈×C₁₉	—	4	1	no	—
245	C₈×C₁₉	—	4	1	no	—
246	C₈×C₁₉	—	4	1	no	—
247	C₈×C₁₉	#137	1	2	yes	—
248	#3255	C₂×C₁₉	1	1	yes	characteristic
249	#3237	C₂×C₁₉	1	1	yes	characteristic
250	#3185	C₂×C₁₉	1	1	yes	characteristic
251	#2962	C₂×C₁₉	1	1	yes	characteristic
252	#1704	C₂×C₁₉	1	1	yes	characteristic, complemented
253	#1700	C₂×C₁₉	1	1	yes	characteristic, complemented
254	#1692	C₂×C₁₉	1	1	yes	characteristic, complemented
255	#1690	C₂×C₁₉	1	1	yes	characteristic, complemented
256	#1684	C₂×C₁₉	1	1	yes	characteristic, complemented
257	#1680	C₂×C₁₉	1	1	yes	characteristic, complemented
258	#1672	C₂×C₁₉	1	1	yes	characteristic, complemented
259	#1670	C₂×C₁₉	1	1	yes	characteristic, complemented
260	#1569	C₂×C₁₉	1	1	yes	characteristic
261	#1552	C₂×C₁₉	1	1	yes	characteristic
262	#1550	C₂×C₁₉	1	1	yes	characteristic
263	C₂²×C₁₉	—	2	1	no	—
264	C₂²×C₁₉	—	2	1	no	—
265	C₂²×C₁₉	—	2	1	no	—
266	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
267	C₄×C₁₉	—	2	1	no	—
268	C₄×C₁₉	—	2	1	no	—
269	C₄×C₁₉	—	2	1	no	—
270	C₄×C₁₉	—	2	1	no	—
271	C₄×C₁₉	—	4	1	no	—
272	C₄×C₁₉	—	4	1	no	—
273	C₄×C₁₉	—	4	1	no	—
274	C₄×C₁₉	—	4	1	no	—
275	C₄×C₁₉	—	8	1	no	—
276	C₄×C₁₉	—	8	1	no	—
277	C₄×C₁₉	—	8	1	no	—
278	C₄×C₁₉	—	8	1	no	—
279	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
280	C₄×C₁₉	#575	1	1	yes	characteristic
281	C₄×C₁₉	#577	1	1	yes	characteristic
282	C₄×C₁₉	#578	1	1	yes	characteristic
283	#533	C₂²×C₁₉	1	1	yes	characteristic
284	#533	C₂²×C₁₉	1	1	yes	characteristic
285	#533	C₂²×C₁₉	1	1	yes	characteristic
286	#501	—	2	1	no	—
287	#498	C₂²×C₁₉	1	1	yes	characteristic
288	#494	C₂²×C₁₉	1	1	yes	characteristic
289	#491	—	2	1	no	—
290	#487	C₂²×C₁₉	1	1	yes	characteristic
291	#487	C₂²×C₁₉	1	1	yes	characteristic
292	#485	—	2	1	no	—
293	#485	—	2	1	no	—
294	#477	C₂²×C₁₉	1	1	yes	characteristic
295	#477	C₂²×C₁₉	1	1	yes	characteristic
296	#475	—	2	1	no	—
297	#475	C₂²×C₁₉	1	1	yes	characteristic
298	#475	C₂²×C₁₉	1	1	yes	characteristic
299	#475	C₂²×C₁₉	1	1	yes	characteristic
300	#475	C₂²×C₁₉	1	1	yes	characteristic
301	#470	—	2	1	no	—
302	#470	—	2	1	no	—
303	#470	—	2	1	no	—
304	#470	—	2	1	no	—
305	#462	—	2	1	no	—
306	#462	C₂²×C₁₉	1	1	yes	characteristic
307	#462	C₂²×C₁₉	1	1	yes	characteristic
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	#432	C₂²×C₁₉	1	1	yes	characteristic
317	#424	—	2	1	no	—
318	#423	C₂²×C₁₉	1	1	yes	characteristic
319	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
320	#405	—	2	1	no	—
321	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
322	#335	C₂²×C₁₉	1	1	yes	characteristic
323	#335	C₂²×C₁₉	1	1	yes	characteristic
324	#334	C₂²×C₁₉	1	1	yes	characteristic
325	#334	C₂²×C₁₉	1	1	yes	characteristic
326	#333	C₂²×C₁₉	1	1	yes	characteristic
327	#333	C₂²×C₁₉	1	1	yes	characteristic
328	#332	C₂²×C₁₉	1	1	yes	characteristic
329	#332	C₂²×C₁₉	1	1	yes	characteristic
330	#332	C₂²×C₁₉	1	1	yes	characteristic
331	#332	C₂²×C₁₉	1	1	yes	characteristic
332	#332	C₂²×C₁₉	1	1	yes	characteristic
333	#332	C₂²×C₁₉	1	1	yes	characteristic
334	C₂×C₁₉	—	4	1	no	—
335	C₂×C₁₉	#3037	1	1	yes	characteristic
336	C₂×C₁₉	#3063	1	1	yes	characteristic
337	C₂×C₁₉	#3069	1	1	yes	characteristic
338	C₂×Q₁₆	—	2	1	no	—
339	C₂×Q₁₆	—	2	1	no	—
340	C₂×Q₁₆	—	2	1	no	—
341	C₂×Q₁₆	—	2	1	no	—
342	C₂×M₁₆	—	2	1	no	—
343	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
344	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
345	C₂²×C₈	—	2	1	no	—
346	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
347	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
348	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
349	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
350	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
351	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
352	#125	—	2	1	no	—
353	#125	—	2	1	no	—
354	#125	—	2	1	no	—
355	C₂²⋊Q₈	—	2	1	no	—
356	C₂²⋊Q₈	—	2	1	no	—
357	C₂²⋊Q₈	—	2	1	no	—
358	C₂²⋊Q₈	—	2	1	no	—
359	C₂²⋊Q₈	—	2	1	no	—
360	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
361	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
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	C₂³×C₁₉	1	1	yes	characteristic
368	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
369	#117	—	2	1	no	—
370	#117	—	2	1	no	—
371	#117	—	2	1	no	—
372	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
373	#107	—	2	1	no	—
374	#107	—	2	1	no	—
375	#106	—	2	1	no	—
376	#106	—	2	1	no	—
377	#106	—	2	1	no	—
378	#106	—	2	1	no	—
379	#106	—	2	1	no	—
380	#106	—	2	1	no	—
381	C₄⋊C₈	—	2	1	no	—
382	C₄⋊C₈	—	2	1	no	—
383	C₄⋊C₈	—	2	1	no	—
384	C₄⋊C₈	—	2	1	no	—
385	C₄⋊C₈	—	2	1	no	—
386	C₄⋊C₈	—	2	1	no	—
387	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
388	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
389	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
390	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
391	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
392	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
393	#103	—	2	1	no	—
394	#103	—	2	1	no	—
395	#103	—	2	1	no	—
396	#103	—	2	1	no	—
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	C₂²⋊C₈	—	2	1	no	—
406	#97	—	2	1	no	—
407	#97	—	2	1	no	—
408	#97	—	2	1	no	—
409	#97	D₄×C₁₉	1	1	yes	characteristic
410	#97	D₄×C₁₉	1	1	yes	characteristic
411	C₄×C₈	—	2	1	no	—
412	C₄×C₈	—	2	1	no	—
413	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
414	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
415	C₁₉	#19375	1	1	yes	characteristic, direct product factor, Sylow
416	C₂×Q₈	—	2	1	no	—
417	C₂×Q₈	—	2	1	no	—
418	C₂×Q₈	—	2	1	no	—
419	C₂×Q₈	—	2	1	no	—
420	C₂×Q₈	—	2	1	no	—
421	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
422	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
423	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
424	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
425	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
426	Q₁₆	—	4	2	no	—
427	Q₁₆	—	4	2	no	—
428	Q₁₆	—	8	1	no	—
429	Q₁₆	—	8	1	no	—
430	M₁₆	—	2	2	no	—
431	M₁₆	—	4	1	no	—
432	M₁₆	—	8	1	no	—
433	C₂×C₈	—	2	1	no	—
434	C₂×C₈	—	2	1	no	—
435	C₂×C₈	—	2	1	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	4	2	no	—
440	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
441	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
442	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
443	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	1	no	—
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	—	4	1	no	—
460	C₄⋊C₄	—	4	1	no	—
461	C₄⋊C₄	—	4	1	no	—
462	C₄⋊C₄	—	4	1	no	—
463	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
464	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
465	C₂²⋊C₄	—	2	1	no	—
466	C₂²⋊C₄	—	2	1	no	—
467	C₂²⋊C₄	—	4	1	no	—
468	C₂²⋊C₄	—	4	1	no	—
469	C₄²	—	2	1	no	—
470	C₄²	—	2	1	no	—
471	C₄²	—	4	1	no	—
472	C₄²	—	4	1	no	—
473	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
474	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
475	C₄²	#41×C₁₉	1	1	yes	characteristic
476	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
477	C₂³	C₁₉×#121	1	1	yes	characteristic
478	Q₈	—	2	1	no	—
479	Q₈	—	2	1	no	—
480	Q₈	—	2	1	no	—
481	Q₈	—	2	1	no	—
482	Q₈	—	4	1	no	—
483	Q₈	—	4	1	no	—
484	Q₈	—	4	1	no	—
485	Q₈	—	4	1	no	—
486	Q₈	—	4	1	no	—
487	Q₈	—	4	1	no	—
488	Q₈	—	8	1	no	—
489	Q₈	—	8	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	4	1	no	—
499	C₂×C₄	—	4	1	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
504	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
505	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
506	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
507	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
508	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
509	C₈	—	2	1	no	—
510	C₈	—	2	1	no	—
511	C₈	—	2	1	no	—
512	C₈	—	4	1	no	—
513	C₈	—	4	1	no	—
514	C₈	—	4	1	no	—
515	C₈	—	4	1	no	—
516	C₈	—	4	1	no	—
517	C₈	—	4	1	no	—
518	C₈	C₁₉×#137	1	2	yes	—
519	C₂²	—	2	1	no	—
520	C₂²	—	2	1	no	—
521	C₂²	—	2	1	no	—
522	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
523	C₄	—	2	1	no	—
524	C₄	—	2	1	no	—
525	C₄	—	2	1	no	—
526	C₄	—	2	1	no	—
527	C₄	—	4	1	no	—
528	C₄	—	4	1	no	—
529	C₄	—	4	1	no	—
530	C₄	—	4	1	no	—
531	C₄	—	8	1	no	—
532	C₄	—	8	1	no	—
533	C₄	—	8	1	no	—
534	C₄	—	8	1	no	—
535	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
536	C₄	C₁₉×#575	1	1	yes	characteristic
537	C₄	C₁₉×#577	1	1	yes	characteristic
538	C₄	C₁₉×#578	1	1	yes	characteristic
539	C₂	—	4	1	no	—
540	C₂	C₁₉×#3037	1	1	yes	characteristic
541	C₂	C₁₉×#3063	1	1	yes	characteristic
542	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
205. #19375	C₁₉	direct (N × H)
252. #1704	C₂×C₁₉	semidirect
253. #1700	C₂×C₁₉	semidirect
254. #1692	C₂×C₁₉	semidirect
255. #1690	C₂×C₁₉	semidirect
256. #1684	C₂×C₁₉	semidirect
257. #1680	C₂×C₁₉	semidirect
258. #1672	C₂×C₁₉	semidirect
259. #1670	C₂×C₁₉	semidirect
415. C₁₉	#19375	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×#3255	2
C₁₉×#3237	2
C₁₉×#3185	2
C₁₉×#2962	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×#1552	2
C₁₉×#1550	2
#19375	19

Subgroups — C19×#19375 #18025334

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19375 #18025334