Subgroups — C₁₉×#18370 #18024329

Order 4864.

1024 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3506	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3215	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3213	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2631	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1606	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1600	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1515	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1514	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1466	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#559	—	2	2	no	—
11	C₁₉×#556	—	2	1	no	—
12	C₁₉×#555	—	2	1	no	—
13	C₁₉×#553	—	2	2	no	—
14	C₁₉×#550	—	2	1	no	—
15	C₁₉×#547	—	2	1	no	—
16	C₁₉×#538	C₂²	1	4	yes	—
17	C₁₉×#535	—	2	1	no	—
18	C₁₉×#533	C₂²	1	1	yes	characteristic
19	C₁₉×#532	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
21	C₁₉×#525	—	2	2	no	—
22	C₁₉×#520	—	2	1	no	—
23	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#497	—	2	1	no	—
25	C₁₉×#496	—	2	1	no	—
26	C₁₉×#489	—	2	1	no	—
27	C₁₉×#489	—	2	1	no	—
28	C₁₉×#464	—	2	2	no	—
29	C₁₉×#463	—	2	2	no	—
30	C₁₉×#451	C₂²	1	2	yes	—
31	C₁₉×#450	C₂²	1	2	yes	—
32	C₁₉×#448	C₂²	1	2	yes	—
33	C₁₉×#447	C₂²	1	2	yes	—
34	C₁₉×#432	C₂²	1	1	yes	characteristic
35	C₁₉×#432	C₂²	1	1	yes	characteristic
36	C₁₉×#397	—	2	1	no	—
37	C₁₉×#393	C₂²	1	2	yes	—
38	C₁₉×#392	—	2	1	no	—
39	C₁₉×#392	C₂²	1	2	yes	—
40	C₁₉×#386	—	2	2	no	—
41	C₁₉×#383	C₂²	1	1	yes	characteristic
42	C₁₉×#328	C₂²	1	4	yes	—
43	C₁₉×#327	C₂²	1	4	yes	—
44	C₁₉×#323	C₂²	1	4	yes	—
45	C₂×#41×C₁₉	—	2	2	no	—
46	C₂×#41×C₁₉	—	2	1	no	—
47	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
48	C₂²×D₄×C₁₉	—	2	2	no	—
49	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
50	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₁₉	D₄	1	2	yes	—
52	C₂×Q₁₆×C₁₉	—	2	2	no	—
53	C₂×SD₁₆×C₁₉	—	2	2	no	—
54	C₂×SD₁₆×C₁₉	—	2	2	no	—
55	C₂×D₈×C₁₉	—	2	2	no	—
56	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic, complemented
57	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic, complemented
58	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic, complemented
59	C₁₉×#127	—	2	2	no	—
60	C₁₉×#127	D₄	1	1	yes	characteristic, complemented
61	C₁₉×#126	—	2	4	no	—
62	C₁₉×#125	—	2	1	no	—
63	C₁₉×#124	—	2	2	no	—
64	C₁₉×#124	—	2	4	no	—
65	C₁₉×#124	—	2	1	no	—
66	C₁₉×#124	—	2	1	no	—
67	C₁₉×#124	—	2	1	no	—
68	C₁₉×#124	—	2	1	no	—
69	C₁₉×#124	—	2	1	no	—
70	C₁₉×#123	—	2	4	no	—
71	C₁₉×#123	—	2	4	no	—
72	C₁₉×C₂²⋊Q₈	—	2	2	no	—
73	C₁₉×C₂²⋊Q₈	—	2	1	no	—
74	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
75	C₁₉×#121	—	2	2	no	—
76	C₁₉×#121	—	2	2	no	—
77	C₁₉×#121	—	2	2	no	—
78	C₁₉×#121	—	2	4	no	—
79	C₁₉×#121	—	2	1	no	—
80	C₁₉×#121	C₂³	1	2	yes	—
81	C₁₉×#120	—	2	4	no	—
82	C₄×Q₈×C₁₉	—	2	2	no	—
83	C₄×Q₈×C₁₉	—	2	1	no	—
84	C₄×Q₈×C₁₉	D₄	1	2	yes	complemented
85	C₄×D₄×C₁₉	—	2	2	no	—
86	C₄×D₄×C₁₉	—	2	4	no	—
87	C₄×D₄×C₁₉	—	2	4	no	—
88	C₄×D₄×C₁₉	—	2	1	no	—
89	C₄×D₄×C₁₉	—	2	1	no	—
90	C₄×D₄×C₁₉	—	2	1	no	—
91	C₄×D₄×C₁₉	—	2	1	no	—
92	C₄×D₄×C₁₉	—	2	1	no	—
93	C₄×D₄×C₁₉	D₄	1	2	yes	complemented
94	C₁₉×#117	—	2	2	no	—
95	C₁₉×#117	—	2	2	no	—
96	C₁₉×#117	—	2	1	no	—
97	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
98	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
99	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
101	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
102	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
103	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
104	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
105	C₁₉×C₄⋊C₈	—	2	1	no	—
106	C₁₉×C₄⋊C₈	—	2	1	no	—
107	C₁₉×#103	—	2	2	no	—
108	C₁₉×#103	—	2	2	no	—
109	C₁₉×#102	—	2	2	no	—
110	C₁₉×#102	—	2	2	no	—
111	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
112	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
113	C₁₉×#97	—	2	1	no	—
114	C₁₉×#97	—	2	1	no	—
115	C₁₉×#95	—	2	1	no	—
116	C₁₉×#95	—	2	1	no	—
117	C₁₉×#95	—	2	2	no	—
118	C₁₉×#95	C₂³	1	2	yes	—
119	C₂⁴×C₁₉	—	2	1	no	—
120	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
121	#41×C₁₉	—	4	4	no	—
122	#41×C₁₉	—	8	4	no	—
123	C₂×Q₈×C₁₉	—	2	1	no	—
124	C₂×Q₈×C₁₉	—	2	1	no	—
125	C₂×Q₈×C₁₉	—	2	1	no	—
126	C₂×Q₈×C₁₉	—	2	1	no	—
127	C₂×Q₈×C₁₉	—	8	1	no	—
128	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
129	C₂×D₄×C₁₉	—	2	2	no	—
130	C₂×D₄×C₁₉	—	2	4	no	—
131	C₂×D₄×C₁₉	—	2	4	no	—
132	C₂×D₄×C₁₉	—	2	1	no	—
133	C₂×D₄×C₁₉	—	2	1	no	—
134	C₂×D₄×C₁₉	—	2	1	no	—
135	C₂×D₄×C₁₉	—	2	1	no	—
136	C₂×D₄×C₁₉	—	2	1	no	—
137	C₂×D₄×C₁₉	—	2	1	no	—
138	C₂×D₄×C₁₉	—	4	2	no	—
139	C₂×D₄×C₁₉	—	4	4	no	—
140	C₂×D₄×C₁₉	—	8	1	no	—
141	C₂×D₄×C₁₉	—	8	2	no	—
142	C₂×D₄×C₁₉	—	8	2	no	—
143	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₁₉	—	2	4	no	—
145	C₂²×C₄×C₁₉	—	2	2	no	—
146	C₂²×C₄×C₁₉	—	2	2	no	—
147	C₂²×C₄×C₁₉	—	2	2	no	—
148	C₂²×C₄×C₁₉	—	2	1	no	—
149	C₂²×C₄×C₁₉	—	2	2	no	—
150	C₂²×C₄×C₁₉	—	8	2	no	—
151	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
153	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
155	Q₁₆×C₁₉	—	8	2	no	—
156	SD₁₆×C₁₉	—	8	2	no	—
157	SD₁₆×C₁₉	—	8	2	no	—
158	D₈×C₁₉	—	8	2	no	—
159	C₂×C₈×C₁₉	—	2	2	no	—
160	C₂×C₈×C₁₉	—	2	2	no	—
161	C₄⋊C₄×C₁₉	—	2	4	no	—
162	C₄⋊C₄×C₁₉	—	2	1	no	—
163	C₄⋊C₄×C₁₉	—	2	1	no	—
164	C₄⋊C₄×C₁₉	—	2	1	no	—
165	C₄⋊C₄×C₁₉	—	2	1	no	—
166	C₄⋊C₄×C₁₉	—	2	1	no	—
167	C₄⋊C₄×C₁₉	—	2	1	no	—
168	C₄⋊C₄×C₁₉	—	2	2	no	—
169	C₄⋊C₄×C₁₉	—	2	2	no	—
170	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
171	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
172	C₂²⋊C₄×C₁₉	—	2	4	no	—
173	C₂²⋊C₄×C₁₉	—	2	4	no	—
174	C₂²⋊C₄×C₁₉	—	2	4	no	—
175	C₂²⋊C₄×C₁₉	—	2	2	no	—
176	C₂²⋊C₄×C₁₉	—	2	2	no	—
177	C₂²⋊C₄×C₁₉	—	2	2	no	—
178	C₂²⋊C₄×C₁₉	—	2	2	no	—
179	C₂²⋊C₄×C₁₉	—	2	2	no	—
180	C₂²⋊C₄×C₁₉	—	4	1	no	—
181	C₂²⋊C₄×C₁₉	—	4	1	no	—
182	C₂²⋊C₄×C₁₉	—	4	1	no	—
183	C₂²⋊C₄×C₁₉	—	4	1	no	—
184	C₂²⋊C₄×C₁₉	—	8	2	no	—
185	C₂²⋊C₄×C₁₉	—	8	2	no	—
186	C₄²×C₁₉	—	2	4	no	—
187	C₄²×C₁₉	—	2	2	no	—
188	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
189	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
190	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
191	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
192	#18370	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
193	C₂³×C₁₉	—	2	2	no	—
194	C₂³×C₁₉	—	2	2	no	—
195	C₂³×C₁₉	—	2	2	no	—
196	C₂³×C₁₉	—	2	2	no	—
197	C₂³×C₁₉	—	4	2	no	—
198	C₂³×C₁₉	—	4	2	no	—
199	C₂³×C₁₉	—	4	1	no	—
200	C₂³×C₁₉	—	4	1	no	—
201	C₂³×C₁₉	—	4	2	no	—
202	C₂³×C₁₉	—	4	1	no	—
203	C₂³×C₁₉	—	4	2	no	—
204	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
205	Q₈×C₁₉	—	4	2	no	—
206	Q₈×C₁₉	—	4	2	no	—
207	Q₈×C₁₉	—	4	2	no	—
208	Q₈×C₁₉	—	4	2	no	—
209	Q₈×C₁₉	—	4	2	no	—
210	D₄×C₁₉	—	4	2	no	—
211	D₄×C₁₉	—	4	2	no	—
212	D₄×C₁₉	—	4	2	no	—
213	D₄×C₁₉	—	4	2	no	—
214	D₄×C₁₉	—	4	2	no	—
215	D₄×C₁₉	—	4	2	no	—
216	D₄×C₁₉	—	4	2	no	—
217	D₄×C₁₉	—	4	4	no	—
218	D₄×C₁₉	—	8	4	no	—
219	D₄×C₁₉	—	8	4	no	—
220	D₄×C₁₉	—	8	8	no	—
221	C₂×C₄×C₁₉	—	2	2	no	—
222	C₂×C₄×C₁₉	—	2	2	no	—
223	C₂×C₄×C₁₉	—	2	2	no	—
224	C₂×C₄×C₁₉	—	2	2	no	—
225	C₂×C₄×C₁₉	—	2	2	no	—
226	C₂×C₄×C₁₉	—	4	1	no	—
227	C₂×C₄×C₁₉	—	4	1	no	—
228	C₂×C₄×C₁₉	—	4	4	no	—
229	C₂×C₄×C₁₉	—	4	4	no	—
230	C₂×C₄×C₁₉	—	4	2	no	—
231	C₂×C₄×C₁₉	—	4	2	no	—
232	C₂×C₄×C₁₉	—	4	2	no	—
233	C₂×C₄×C₁₉	—	4	2	no	—
234	C₂×C₄×C₁₉	—	4	1	no	—
235	C₂×C₄×C₁₉	—	4	2	no	—
236	C₂×C₄×C₁₉	—	8	2	no	—
237	C₂×C₄×C₁₉	—	8	4	no	—
238	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
239	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
240	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
241	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
242	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
243	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
244	C₈×C₁₉	—	4	2	no	—
245	C₈×C₁₉	—	4	2	no	—
246	#3506	C₂×C₁₉	1	1	yes	characteristic, complemented
247	#3215	C₂×C₁₉	1	1	yes	characteristic, complemented
248	#3213	C₂×C₁₉	1	1	yes	characteristic, complemented
249	#2631	C₂×C₁₉	1	1	yes	characteristic, complemented
250	#1606	C₂×C₁₉	1	4	yes	complemented
251	#1600	C₂×C₁₉	1	4	yes	complemented
252	#1515	C₂×C₁₉	1	1	yes	characteristic, complemented
253	#1514	C₂×C₁₉	1	1	yes	characteristic, complemented
254	#1466	C₂×C₁₉	1	1	yes	characteristic, complemented
255	C₂²×C₁₉	—	2	1	no	—
256	C₂²×C₁₉	—	2	1	no	—
257	C₂²×C₁₉	—	4	4	no	—
258	C₂²×C₁₉	—	4	2	no	—
259	C₂²×C₁₉	—	4	2	no	—
260	C₂²×C₁₉	—	4	2	no	—
261	C₂²×C₁₉	—	4	2	no	—
262	C₂²×C₁₉	—	4	2	no	—
263	C₂²×C₁₉	—	4	2	no	—
264	C₂²×C₁₉	—	8	2	no	—
265	C₂²×C₁₉	—	8	2	no	—
266	C₂²×C₁₉	—	8	2	no	—
267	C₂²×C₁₉	—	8	1	no	—
268	C₂²×C₁₉	—	8	1	no	—
269	C₂²×C₁₉	—	8	1	no	—
270	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
271	C₂²×C₁₉	#575	1	2	yes	—
272	C₄×C₁₉	—	2	1	no	—
273	C₄×C₁₉	—	2	1	no	—
274	C₄×C₁₉	—	2	1	no	—
275	C₄×C₁₉	—	2	1	no	—
276	C₄×C₁₉	—	2	1	no	—
277	C₄×C₁₉	—	2	1	no	—
278	C₄×C₁₉	—	4	2	no	—
279	C₄×C₁₉	—	4	2	no	—
280	C₄×C₁₉	—	4	2	no	—
281	C₄×C₁₉	—	4	2	no	—
282	C₄×C₁₉	—	8	2	no	—
283	C₄×C₁₉	—	8	1	no	—
284	#559	—	2	2	no	—
285	#556	—	2	1	no	—
286	#555	—	2	1	no	—
287	#553	—	2	2	no	—
288	#550	—	2	1	no	—
289	#547	—	2	1	no	—
290	#538	C₂²×C₁₉	1	4	yes	—
291	#535	—	2	1	no	—
292	#533	C₂²×C₁₉	1	1	yes	characteristic
293	#532	C₂²×C₁₉	1	1	yes	characteristic
294	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
295	#525	—	2	2	no	—
296	#520	—	2	1	no	—
297	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
298	#497	—	2	1	no	—
299	#496	—	2	1	no	—
300	#489	—	2	1	no	—
301	#489	—	2	1	no	—
302	#464	—	2	2	no	—
303	#463	—	2	2	no	—
304	#451	C₂²×C₁₉	1	2	yes	—
305	#450	C₂²×C₁₉	1	2	yes	—
306	#448	C₂²×C₁₉	1	2	yes	—
307	#447	C₂²×C₁₉	1	2	yes	—
308	#432	C₂²×C₁₉	1	1	yes	characteristic
309	#432	C₂²×C₁₉	1	1	yes	characteristic
310	#397	—	2	1	no	—
311	#393	C₂²×C₁₉	1	2	yes	—
312	#392	—	2	1	no	—
313	#392	C₂²×C₁₉	1	2	yes	—
314	#386	—	2	2	no	—
315	#383	C₂²×C₁₉	1	1	yes	characteristic
316	#328	C₂²×C₁₉	1	4	yes	—
317	#327	C₂²×C₁₉	1	4	yes	—
318	#323	C₂²×C₁₉	1	4	yes	—
319	C₂×C₁₉	—	2	2	no	—
320	C₂×C₁₉	—	8	2	no	—
321	C₂×C₁₉	—	8	2	no	—
322	C₂×C₁₉	—	16	1	no	—
323	C₂×C₁₉	#3005	1	1	yes	characteristic
324	C₂×C₁₉	#3019	1	1	yes	characteristic
325	C₂×C₁₉	#3027	1	1	yes	characteristic
326	C₂×#41	—	2	2	no	—
327	C₂×#41	—	2	1	no	—
328	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
329	C₂²×D₄	—	2	2	no	—
330	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
331	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
332	C₂³×C₄	D₄×C₁₉	1	2	yes	—
333	C₂×Q₁₆	—	2	2	no	—
334	C₂×SD₁₆	—	2	2	no	—
335	C₂×SD₁₆	—	2	2	no	—
336	C₂×D₈	—	2	2	no	—
337	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic, complemented
338	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic, complemented
339	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic, complemented
340	#127	—	2	2	no	—
341	#127	D₄×C₁₉	1	1	yes	characteristic, complemented
342	#126	—	2	4	no	—
343	#125	—	2	1	no	—
344	#124	—	2	2	no	—
345	#124	—	2	4	no	—
346	#124	—	2	1	no	—
347	#124	—	2	1	no	—
348	#124	—	2	1	no	—
349	#124	—	2	1	no	—
350	#124	—	2	1	no	—
351	#123	—	2	4	no	—
352	#123	—	2	4	no	—
353	C₂²⋊Q₈	—	2	2	no	—
354	C₂²⋊Q₈	—	2	1	no	—
355	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
356	#121	—	2	2	no	—
357	#121	—	2	2	no	—
358	#121	—	2	2	no	—
359	#121	—	2	4	no	—
360	#121	—	2	1	no	—
361	#121	C₂³×C₁₉	1	2	yes	—
362	#120	—	2	4	no	—
363	C₄×Q₈	—	2	2	no	—
364	C₄×Q₈	—	2	1	no	—
365	C₄×Q₈	D₄×C₁₉	1	2	yes	complemented
366	C₄×D₄	—	2	2	no	—
367	C₄×D₄	—	2	4	no	—
368	C₄×D₄	—	2	4	no	—
369	C₄×D₄	—	2	1	no	—
370	C₄×D₄	—	2	1	no	—
371	C₄×D₄	—	2	1	no	—
372	C₄×D₄	—	2	1	no	—
373	C₄×D₄	—	2	1	no	—
374	C₄×D₄	D₄×C₁₉	1	2	yes	complemented
375	#117	—	2	2	no	—
376	#117	—	2	2	no	—
377	#117	—	2	1	no	—
378	C₂×C₄⋊C₄	—	2	2	no	—
379	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
380	C₂×C₂²⋊C₄	—	2	1	no	—
381	C₂×C₂²⋊C₄	—	2	1	no	—
382	C₂×C₂²⋊C₄	—	2	2	no	—
383	C₂×C₂²⋊C₄	—	2	2	no	—
384	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
385	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
386	C₄⋊C₈	—	2	1	no	—
387	C₄⋊C₈	—	2	1	no	—
388	#103	—	2	2	no	—
389	#103	—	2	2	no	—
390	#102	—	2	2	no	—
391	#102	—	2	2	no	—
392	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
393	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
394	#97	—	2	1	no	—
395	#97	—	2	1	no	—
396	#95	—	2	1	no	—
397	#95	—	2	1	no	—
398	#95	—	2	2	no	—
399	#95	C₂³×C₁₉	1	2	yes	—
400	C₁₉	#18370	1	1	yes	characteristic, direct product factor, Sylow
401	C₂⁴	—	2	1	no	—
402	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
403	#41	—	4	4	no	—
404	#41	—	8	4	no	—
405	C₂×Q₈	—	2	1	no	—
406	C₂×Q₈	—	2	1	no	—
407	C₂×Q₈	—	2	1	no	—
408	C₂×Q₈	—	2	1	no	—
409	C₂×Q₈	—	8	1	no	—
410	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	—	2	4	no	—
413	C₂×D₄	—	2	4	no	—
414	C₂×D₄	—	2	1	no	—
415	C₂×D₄	—	2	1	no	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	—	2	1	no	—
418	C₂×D₄	—	2	1	no	—
419	C₂×D₄	—	2	1	no	—
420	C₂×D₄	—	4	2	no	—
421	C₂×D₄	—	4	4	no	—
422	C₂×D₄	—	8	1	no	—
423	C₂×D₄	—	8	2	no	—
424	C₂×D₄	—	8	2	no	—
425	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
426	C₂²×C₄	—	2	4	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	8	2	no	—
433	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
434	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
435	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
436	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
437	Q₁₆	—	8	2	no	—
438	SD₁₆	—	8	2	no	—
439	SD₁₆	—	8	2	no	—
440	D₈	—	8	2	no	—
441	C₂×C₈	—	2	2	no	—
442	C₂×C₈	—	2	2	no	—
443	C₄⋊C₄	—	2	4	no	—
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	2	no	—
451	C₄⋊C₄	—	2	2	no	—
452	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
453	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
454	C₂²⋊C₄	—	2	4	no	—
455	C₂²⋊C₄	—	2	4	no	—
456	C₂²⋊C₄	—	2	4	no	—
457	C₂²⋊C₄	—	2	2	no	—
458	C₂²⋊C₄	—	2	2	no	—
459	C₂²⋊C₄	—	2	2	no	—
460	C₂²⋊C₄	—	2	2	no	—
461	C₂²⋊C₄	—	2	2	no	—
462	C₂²⋊C₄	—	4	1	no	—
463	C₂²⋊C₄	—	4	1	no	—
464	C₂²⋊C₄	—	4	1	no	—
465	C₂²⋊C₄	—	4	1	no	—
466	C₂²⋊C₄	—	8	2	no	—
467	C₂²⋊C₄	—	8	2	no	—
468	C₄²	—	2	4	no	—
469	C₄²	—	2	2	no	—
470	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
471	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
472	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
473	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
474	C₂³	—	2	2	no	—
475	C₂³	—	2	2	no	—
476	C₂³	—	2	2	no	—
477	C₂³	—	2	2	no	—
478	C₂³	—	4	2	no	—
479	C₂³	—	4	2	no	—
480	C₂³	—	4	1	no	—
481	C₂³	—	4	1	no	—
482	C₂³	—	4	2	no	—
483	C₂³	—	4	1	no	—
484	C₂³	—	4	2	no	—
485	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
486	Q₈	—	4	2	no	—
487	Q₈	—	4	2	no	—
488	Q₈	—	4	2	no	—
489	Q₈	—	4	2	no	—
490	Q₈	—	4	2	no	—
491	D₄	—	4	2	no	—
492	D₄	—	4	2	no	—
493	D₄	—	4	2	no	—
494	D₄	—	4	2	no	—
495	D₄	—	4	2	no	—
496	D₄	—	4	2	no	—
497	D₄	—	4	2	no	—
498	D₄	—	4	4	no	—
499	D₄	—	8	4	no	—
500	D₄	—	8	4	no	—
501	D₄	—	8	8	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	4	4	no	—
510	C₂×C₄	—	4	4	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	—	4	2	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	4	2	no	—
517	C₂×C₄	—	8	2	no	—
518	C₂×C₄	—	8	4	no	—
519	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
520	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
521	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
522	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
523	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
524	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
525	C₈	—	4	2	no	—
526	C₈	—	4	2	no	—
527	C₂²	—	2	1	no	—
528	C₂²	—	2	1	no	—
529	C₂²	—	4	4	no	—
530	C₂²	—	4	2	no	—
531	C₂²	—	4	2	no	—
532	C₂²	—	4	2	no	—
533	C₂²	—	4	2	no	—
534	C₂²	—	4	2	no	—
535	C₂²	—	4	2	no	—
536	C₂²	—	8	2	no	—
537	C₂²	—	8	2	no	—
538	C₂²	—	8	2	no	—
539	C₂²	—	8	1	no	—
540	C₂²	—	8	1	no	—
541	C₂²	—	8	1	no	—
542	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
543	C₂²	C₁₉×#575	1	2	yes	—
544	C₄	—	2	1	no	—
545	C₄	—	2	1	no	—
546	C₄	—	2	1	no	—
547	C₄	—	2	1	no	—
548	C₄	—	2	1	no	—
549	C₄	—	2	1	no	—
550	C₄	—	4	2	no	—
551	C₄	—	4	2	no	—
552	C₄	—	4	2	no	—
553	C₄	—	4	2	no	—
554	C₄	—	8	2	no	—
555	C₄	—	8	1	no	—
556	C₂	—	2	2	no	—
557	C₂	—	8	2	no	—
558	C₂	—	8	2	no	—
559	C₂	—	16	1	no	—
560	C₂	C₁₉×#3005	1	1	yes	characteristic
561	C₂	C₁₉×#3019	1	1	yes	characteristic
562	C₂	C₁₉×#3027	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂²×C₄ ▷ 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×#3506	C₂	semidirect
2. C₁₉×#3215	C₂	semidirect
3. C₁₉×#3213	C₂	semidirect
4. C₁₉×#2631	C₂	semidirect
5. C₁₉×#1606	C₂	semidirect
6. C₁₉×#1600	C₂	semidirect
7. C₁₉×#1515	C₂	semidirect
8. C₁₉×#1514	C₂	semidirect
9. C₁₉×#1466	C₂	semidirect
56. C₁₉×C₄⋊Q₈	D₄	semidirect
57. C₁₉×C₄⋊Q₈	D₄	semidirect
58. C₁₉×C₄⋊Q₈	D₄	semidirect
60. C₁₉×#127	D₄	semidirect
84. C₄×Q₈×C₁₉	D₄	semidirect
93. C₄×D₄×C₁₉	D₄	semidirect
192. #18370	C₁₉	direct (N × H)
246. #3506	C₂×C₁₉	semidirect
247. #3215	C₂×C₁₉	semidirect
248. #3213	C₂×C₁₉	semidirect
249. #2631	C₂×C₁₉	semidirect
250. #1606	C₂×C₁₉	semidirect
251. #1600	C₂×C₁₉	semidirect
252. #1515	C₂×C₁₉	semidirect
253. #1514	C₂×C₁₉	semidirect
254. #1466	C₂×C₁₉	semidirect
337. C₄⋊Q₈	D₄×C₁₉	semidirect
338. C₄⋊Q₈	D₄×C₁₉	semidirect
339. C₄⋊Q₈	D₄×C₁₉	semidirect
341. #127	D₄×C₁₉	semidirect
365. C₄×Q₈	D₄×C₁₉	semidirect
374. C₄×D₄	D₄×C₁₉	semidirect
400. C₁₉	#18370	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×#3506	2
C₁₉×#3215	2
C₁₉×#3213	2
C₁₉×#2631	2
C₁₉×#1606	2
C₁₉×#1600	2
C₁₉×#1515	2
C₁₉×#1514	2
C₁₉×#1466	2
#18370	19

Subgroups — C19×#18370 #18024329

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18370 #18024329