Subgroups — C₁₉×#18984 #18024943

Order 4864.

990 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3529	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3171	C₂	1	2	yes	maximal, complemented
3	C₁₉×#3150	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1661	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1660	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1659	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1657	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1656	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1655	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1525	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1524	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₉×#135	—	2	1	no	—
13	C₂×C₁₉×#135	—	2	1	no	—
14	C₁₉×#563	—	2	1	no	—
15	C₁₉×#563	C₂²	1	1	yes	characteristic
16	C₁₉×#562	—	2	2	no	—
17	C₁₉×#562	C₂²	1	2	yes	—
18	C₁₉×H(3,𝔽₄)	C₂²	1	1	yes	characteristic
19	C₁₉×#560	—	2	1	no	—
20	C₁₉×#560	—	2	2	no	—
21	C₁₉×#532	—	2	1	no	—
22	C₁₉×#532	C₂²	1	1	yes	characteristic
23	C₁₉×#532	C₂²	1	1	yes	characteristic, complemented
24	C₁₉×#529	—	2	2	no	—
25	C₁₉×#529	C₂²	1	2	yes	—
26	C₁₉×#525	—	2	1	no	—
27	C₁₉×#525	—	2	2	no	—
28	C₁₉×#501	C₂²	1	2	yes	complemented
29	C₁₉×#497	—	2	1	no	—
30	C₁₉×#497	C₂²	1	1	yes	characteristic
31	C₁₉×#497	C₂²	1	1	yes	characteristic, complemented
32	C₁₉×#496	—	2	1	no	—
33	C₁₉×#496	C₂²	1	2	yes	—
34	C₁₉×#496	C₂²	1	1	yes	characteristic
35	C₁₉×#496	C₂²	1	1	yes	characteristic, complemented
36	C₁₉×#490	C₂²	1	2	yes	complemented
37	C₁₉×#489	C₂²	1	2	yes	—
38	C₁₉×#469	—	2	2	no	—
39	C₁₉×#468	—	2	2	no	—
40	C₄×SD₁₆×C₁₉	—	2	2	no	—
41	C₄×D₈×C₁₉	—	2	2	no	—
42	C₄×M₁₆×C₁₉	C₂²	1	2	yes	complemented
43	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic, complemented
44	C₁₉×#330	C₂²	1	2	yes	complemented
45	C₁₉×#330	C₂²	1	2	yes	complemented
46	C₁₉×#329	C₂²	1	1	yes	characteristic
47	C₁₉×#329	C₂²	1	2	yes	—
48	C₁₉×#329	C₂²	1	2	yes	—
49	C₁₉×#329	C₂²	1	1	yes	characteristic
50	C₁₉×#329	C₂²	1	2	yes	complemented
51	C₂×#41×C₁₉	—	2	1	no	—
52	C₂×#41×C₁₉	—	2	1	no	—
53	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
54	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
55	C₂³×C₄×C₁₉	—	2	1	no	—
56	C₁₉×#135	—	4	4	no	—
57	C₁₉×#135	—	4	4	no	—
58	C₂×Q₁₆×C₁₉	—	2	1	no	—
59	C₂×Q₁₆×C₁₉	—	2	1	no	—
60	C₂×SD₁₆×C₁₉	—	2	2	no	—
61	C₂×SD₁₆×C₁₉	—	2	1	no	—
62	C₂×SD₁₆×C₁₉	—	2	1	no	—
63	C₂×SD₁₆×C₁₉	—	2	1	no	—
64	C₂×SD₁₆×C₁₉	—	2	1	no	—
65	C₂×D₈×C₁₉	—	2	2	no	—
66	C₂×D₈×C₁₉	—	2	1	no	—
67	C₂×D₈×C₁₉	—	2	1	no	—
68	C₂×M₁₆×C₁₉	—	2	2	no	—
69	C₂²×C₈×C₁₉	—	2	1	no	—
70	C₁₉×C₄⋊Q₈	—	2	1	no	—
71	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
72	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
73	C₁₉×#127	—	2	1	no	—
74	C₁₉×#127	D₄	1	1	yes	characteristic
75	C₁₉×#127	C₂³	1	1	yes	characteristic
76	C₁₉×#126	—	2	2	no	—
77	C₁₉×#126	—	2	2	no	—
78	C₁₉×#126	—	2	2	no	—
79	C₁₉×#125	—	2	2	no	—
80	C₁₉×#125	C₂³	1	2	yes	—
81	C₁₉×#124	—	2	1	no	—
82	C₁₉×#124	—	2	2	no	—
83	C₁₉×#124	—	2	1	no	—
84	C₁₉×#124	—	2	1	no	—
85	C₁₉×#124	C₂³	1	2	yes	—
86	C₁₉×#124	C₂³	1	1	yes	characteristic
87	C₁₉×#124	C₂³	1	1	yes	characteristic
88	C₁₉×#123	—	2	2	no	—
89	C₁₉×#123	—	2	1	no	—
90	C₁₉×#123	—	2	2	no	—
91	C₁₉×#123	—	2	1	no	—
92	C₁₉×#123	—	2	2	no	—
93	C₁₉×#123	—	2	2	no	—
94	C₁₉×#123	—	2	2	no	—
95	C₁₉×C₂²⋊Q₈	—	2	2	no	—
96	C₁₉×C₂²⋊Q₈	—	2	2	no	—
97	C₁₉×C₂²⋊Q₈	—	2	2	no	—
98	C₁₉×C₂²⋊Q₈	—	2	2	no	—
99	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
100	C₁₉×#121	—	2	2	no	—
101	C₁₉×#121	—	2	2	no	—
102	C₁₉×#121	—	2	2	no	—
103	C₁₉×#121	—	2	2	no	—
104	C₁₉×#121	—	2	2	no	—
105	C₁₉×#121	—	2	2	no	—
106	C₁₉×#121	—	2	2	no	—
107	C₁₉×#121	—	2	2	no	—
108	C₁₉×#121	D₄	1	2	yes	—
109	C₁₉×#120	—	2	1	no	—
110	C₁₉×#120	—	2	2	no	—
111	C₁₉×#120	—	2	1	no	—
112	C₁₉×#120	—	2	2	no	—
113	C₄×Q₈×C₁₉	D₄	1	2	yes	—
114	C₄×D₄×C₁₉	—	2	2	no	—
115	C₄×D₄×C₁₉	—	2	2	no	—
116	C₄×D₄×C₁₉	—	2	2	no	—
117	C₄×D₄×C₁₉	—	2	2	no	—
118	C₄×D₄×C₁₉	—	2	2	no	—
119	C₄×D₄×C₁₉	D₄	1	2	yes	—
120	C₁₉×#117	—	2	1	no	—
121	C₁₉×#117	—	2	2	no	—
122	C₂×C₄²×C₁₉	—	2	1	no	—
123	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
124	C₁₉×#107	—	2	2	no	—
125	C₁₉×#106	—	2	2	no	—
126	C₁₉×#103	—	2	2	no	—
127	C₁₉×#102	—	2	2	no	—
128	C₁₉×#102	—	2	2	no	—
129	C₁₉×#102	—	2	2	no	—
130	C₁₉×#97	—	2	1	no	—
131	C₁₉×#97	C₂³	1	1	yes	characteristic
132	C₁₉×#97	C₂³	1	1	yes	characteristic
133	C₁₉×#97	C₂³	1	2	yes	—
134	C₁₉×#97	C₂³	1	2	yes	—
135	C₄×C₈×C₁₉	—	2	2	no	—
136	C₂⁴×C₁₉	—	2	1	no	—
137	#41×C₁₉	—	4	2	no	—
138	#41×C₁₉	—	4	2	no	—
139	#41×C₁₉	—	4	2	no	—
140	#41×C₁₉	—	4	2	no	—
141	#41×C₁₉	—	8	2	no	—
142	C₂×Q₈×C₁₉	—	2	1	no	—
143	C₂×Q₈×C₁₉	—	2	1	no	—
144	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
145	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
146	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
147	C₂×D₄×C₁₉	—	2	2	no	—
148	C₂×D₄×C₁₉	—	2	2	no	—
149	C₂×D₄×C₁₉	—	2	1	no	—
150	C₂×D₄×C₁₉	—	2	2	no	—
151	C₂×D₄×C₁₉	—	2	2	no	—
152	C₂×D₄×C₁₉	—	2	1	no	—
153	C₂×D₄×C₁₉	—	2	1	no	—
154	C₂×D₄×C₁₉	—	2	2	no	—
155	C₂×D₄×C₁₉	—	2	2	no	—
156	C₂×D₄×C₁₉	—	2	1	no	—
157	C₂×D₄×C₁₉	—	4	1	no	—
158	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
159	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
160	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₉	—	2	2	no	—
162	C₂²×C₄×C₁₉	—	2	2	no	—
163	C₂²×C₄×C₁₉	—	2	1	no	—
164	C₂²×C₄×C₁₉	—	2	1	no	—
165	C₂²×C₄×C₁₉	—	2	1	no	—
166	C₂²×C₄×C₁₉	—	2	2	no	—
167	C₂²×C₄×C₁₉	—	4	1	no	—
168	C₂²×C₄×C₁₉	—	8	2	no	—
169	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
171	Q₁₆×C₁₉	—	4	2	no	—
172	Q₁₆×C₁₉	—	4	2	no	—
173	SD₁₆×C₁₉	—	4	4	no	—
174	SD₁₆×C₁₉	—	4	2	no	—
175	SD₁₆×C₁₉	—	4	2	no	—
176	SD₁₆×C₁₉	—	4	2	no	—
177	SD₁₆×C₁₉	—	4	2	no	—
178	D₈×C₁₉	—	4	4	no	—
179	D₈×C₁₉	—	4	2	no	—
180	D₈×C₁₉	—	4	2	no	—
181	M₁₆×C₁₉	—	4	4	no	—
182	C₂×C₈×C₁₉	—	2	4	no	—
183	C₂×C₈×C₁₉	—	2	1	no	—
184	C₂×C₈×C₁₉	—	2	1	no	—
185	C₂×C₈×C₁₉	—	2	2	no	—
186	C₂×C₈×C₁₉	—	2	2	no	—
187	C₄⋊C₄×C₁₉	—	2	2	no	—
188	C₄⋊C₄×C₁₉	—	2	2	no	—
189	C₄⋊C₄×C₁₉	—	2	2	no	—
190	C₄⋊C₄×C₁₉	—	2	2	no	—
191	C₄⋊C₄×C₁₉	—	2	2	no	—
192	C₄⋊C₄×C₁₉	—	2	2	no	—
193	C₄⋊C₄×C₁₉	—	2	2	no	—
194	C₄⋊C₄×C₁₉	—	2	2	no	—
195	C₄⋊C₄×C₁₉	—	2	2	no	—
196	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
197	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
198	C₂²⋊C₄×C₁₉	—	2	1	no	—
199	C₂²⋊C₄×C₁₉	—	2	1	no	—
200	C₂²⋊C₄×C₁₉	—	2	2	no	—
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	2	no	—
205	C₂²⋊C₄×C₁₉	—	2	2	no	—
206	C₂²⋊C₄×C₁₉	—	2	2	no	—
207	C₂²⋊C₄×C₁₉	—	2	2	no	—
208	C₂²⋊C₄×C₁₉	—	2	2	no	—
209	C₂²⋊C₄×C₁₉	—	2	2	no	—
210	C₂²⋊C₄×C₁₉	—	2	2	no	—
211	C₂²⋊C₄×C₁₉	—	4	2	no	—
212	C₄²×C₁₉	—	2	1	no	—
213	C₄²×C₁₉	—	2	1	no	—
214	C₄²×C₁₉	—	2	2	no	—
215	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
216	C₄²×C₁₉	C₂×D₄	1	2	yes	—
217	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
218	#18984	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
219	C₂³×C₁₉	—	2	1	no	—
220	C₂³×C₁₉	—	2	2	no	—
221	C₂³×C₁₉	—	2	1	no	—
222	C₂³×C₁₉	—	4	1	no	—
223	C₂³×C₁₉	—	8	1	no	—
224	C₂³×C₁₉	—	8	2	no	—
225	C₂³×C₁₉	#120	1	1	yes	characteristic
226	Q₈×C₁₉	—	4	1	no	—
227	Q₈×C₁₉	—	4	1	no	—
228	Q₈×C₁₉	—	4	2	no	—
229	Q₈×C₁₉	—	4	1	no	—
230	Q₈×C₁₉	—	4	1	no	—
231	Q₈×C₁₉	—	8	1	no	—
232	D₄×C₁₉	—	4	1	no	—
233	D₄×C₁₉	—	4	1	no	—
234	D₄×C₁₉	—	4	2	no	—
235	D₄×C₁₉	—	4	1	no	—
236	D₄×C₁₉	—	4	1	no	—
237	D₄×C₁₉	—	4	2	no	—
238	D₄×C₁₉	—	4	2	no	—
239	D₄×C₁₉	—	8	2	no	—
240	D₄×C₁₉	—	8	2	no	—
241	D₄×C₁₉	—	8	1	no	—
242	D₄×C₁₉	—	8	1	no	—
243	D₄×C₁₉	—	8	2	no	—
244	D₄×C₁₉	—	8	2	no	—
245	D₄×C₁₉	—	8	2	no	—
246	D₄×C₁₉	—	8	1	no	—
247	D₄×C₁₉	—	8	2	no	—
248	C₂×C₄×C₁₉	—	2	2	no	—
249	C₂×C₄×C₁₉	—	2	2	no	—
250	C₂×C₄×C₁₉	—	2	2	no	—
251	C₂×C₄×C₁₉	—	2	1	no	—
252	C₂×C₄×C₁₉	—	2	1	no	—
253	C₂×C₄×C₁₉	—	2	2	no	—
254	C₂×C₄×C₁₉	—	4	2	no	—
255	C₂×C₄×C₁₉	—	4	2	no	—
256	C₂×C₄×C₁₉	—	4	4	no	—
257	C₂×C₄×C₁₉	—	4	2	no	—
258	C₂×C₄×C₁₉	—	4	1	no	—
259	C₂×C₄×C₁₉	—	8	2	no	—
260	C₂×C₄×C₁₉	—	8	2	no	—
261	C₂×C₄×C₁₉	—	8	1	no	—
262	C₂×C₄×C₁₉	—	8	2	no	—
263	C₂×C₄×C₁₉	#120	1	2	yes	—
264	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
265	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
266	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
267	C₈×C₁₉	—	2	2	no	—
268	C₈×C₁₉	—	2	2	no	—
269	C₈×C₁₉	—	2	4	no	—
270	C₈×C₁₉	—	4	2	no	—
271	#3529	C₂×C₁₉	1	1	yes	characteristic, complemented
272	#3171	C₂×C₁₉	1	2	yes	complemented
273	#3150	C₂×C₁₉	1	1	yes	characteristic, complemented
274	#1661	C₂×C₁₉	1	2	yes	complemented
275	#1660	C₂×C₁₉	1	1	yes	characteristic, complemented
276	#1659	C₂×C₁₉	1	1	yes	characteristic, complemented
277	#1657	C₂×C₁₉	1	1	yes	characteristic, complemented
278	#1656	C₂×C₁₉	1	2	yes	complemented
279	#1655	C₂×C₁₉	1	1	yes	characteristic, complemented
280	#1525	C₂×C₁₉	1	1	yes	characteristic, complemented
281	#1524	C₂×C₁₉	1	2	yes	complemented
282	C₂²×C₁₉	—	2	1	no	—
283	C₂²×C₁₉	—	2	2	no	—
284	C₂²×C₁₉	—	4	1	no	—
285	C₂²×C₁₉	—	4	2	no	—
286	C₂²×C₁₉	—	4	1	no	—
287	C₂²×C₁₉	—	4	2	no	—
288	C₂²×C₁₉	—	4	2	no	—
289	C₂²×C₁₉	—	4	2	no	—
290	C₂²×C₁₉	—	4	2	no	—
291	C₂²×C₁₉	—	8	4	no	—
292	C₂²×C₁₉	—	8	1	no	—
293	C₂²×C₁₉	—	8	2	no	—
294	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
295	C₄×C₁₉	—	2	1	no	—
296	C₄×C₁₉	—	2	2	no	—
297	C₄×C₁₉	—	2	2	no	—
298	C₄×C₁₉	—	4	1	no	—
299	C₄×C₁₉	—	4	2	no	—
300	C₄×C₁₉	—	4	1	no	—
301	C₄×C₁₉	—	4	2	no	—
302	C₄×C₁₉	—	4	2	no	—
303	C₄×C₁₉	—	8	1	no	—
304	C₄×C₁₉	#453	1	2	yes	—
305	C₂×#135	—	2	1	no	—
306	C₂×#135	—	2	1	no	—
307	#563	—	2	1	no	—
308	#563	C₂²×C₁₉	1	1	yes	characteristic
309	#562	—	2	2	no	—
310	#562	C₂²×C₁₉	1	2	yes	—
311	H(3,𝔽₄)	C₂²×C₁₉	1	1	yes	characteristic
312	#560	—	2	1	no	—
313	#560	—	2	2	no	—
314	#532	—	2	1	no	—
315	#532	C₂²×C₁₉	1	1	yes	characteristic
316	#532	C₂²×C₁₉	1	1	yes	characteristic, complemented
317	#529	—	2	2	no	—
318	#529	C₂²×C₁₉	1	2	yes	—
319	#525	—	2	1	no	—
320	#525	—	2	2	no	—
321	#501	C₂²×C₁₉	1	2	yes	complemented
322	#497	—	2	1	no	—
323	#497	C₂²×C₁₉	1	1	yes	characteristic
324	#497	C₂²×C₁₉	1	1	yes	characteristic, complemented
325	#496	—	2	1	no	—
326	#496	C₂²×C₁₉	1	1	yes	characteristic
327	#496	C₂²×C₁₉	1	2	yes	—
328	#496	C₂²×C₁₉	1	1	yes	characteristic, complemented
329	#490	C₂²×C₁₉	1	2	yes	complemented
330	#489	C₂²×C₁₉	1	2	yes	—
331	#469	—	2	2	no	—
332	#468	—	2	2	no	—
333	C₄×SD₁₆	—	2	2	no	—
334	C₄×D₈	—	2	2	no	—
335	C₄×M₁₆	C₂²×C₁₉	1	2	yes	complemented
336	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic, complemented
337	#330	C₂²×C₁₉	1	2	yes	complemented
338	#330	C₂²×C₁₉	1	2	yes	complemented
339	#329	C₂²×C₁₉	1	1	yes	characteristic
340	#329	C₂²×C₁₉	1	2	yes	—
341	#329	C₂²×C₁₉	1	2	yes	—
342	#329	C₂²×C₁₉	1	1	yes	characteristic
343	#329	C₂²×C₁₉	1	2	yes	complemented
344	C₂×C₁₉	—	4	1	no	—
345	C₂×C₁₉	—	8	1	no	—
346	C₂×C₁₉	—	8	1	no	—
347	C₂×C₁₉	—	8	2	no	—
348	C₂×C₁₉	—	16	1	no	—
349	C₂×C₁₉	C₂×#453	1	1	yes	characteristic
350	C₂×C₁₉	#3018	1	2	yes	—
351	C₂×#41	—	2	1	no	—
352	C₂×#41	—	2	1	no	—
353	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
354	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
355	C₂³×C₄	—	2	1	no	—
356	#135	—	4	4	no	—
357	#135	—	4	4	no	—
358	C₂×Q₁₆	—	2	1	no	—
359	C₂×Q₁₆	—	2	1	no	—
360	C₂×SD₁₆	—	2	1	no	—
361	C₂×SD₁₆	—	2	1	no	—
362	C₂×SD₁₆	—	2	2	no	—
363	C₂×SD₁₆	—	2	1	no	—
364	C₂×SD₁₆	—	2	1	no	—
365	C₂×D₈	—	2	1	no	—
366	C₂×D₈	—	2	1	no	—
367	C₂×D₈	—	2	2	no	—
368	C₂×M₁₆	—	2	2	no	—
369	C₂²×C₈	—	2	1	no	—
370	C₄⋊Q₈	—	2	1	no	—
371	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
372	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
373	#127	—	2	1	no	—
374	#127	D₄×C₁₉	1	1	yes	characteristic
375	#127	C₂³×C₁₉	1	1	yes	characteristic
376	#126	—	2	2	no	—
377	#126	—	2	2	no	—
378	#126	—	2	2	no	—
379	#125	—	2	2	no	—
380	#125	C₂³×C₁₉	1	2	yes	—
381	#124	—	2	1	no	—
382	#124	—	2	2	no	—
383	#124	—	2	1	no	—
384	#124	—	2	1	no	—
385	#124	C₂³×C₁₉	1	2	yes	—
386	#124	C₂³×C₁₉	1	1	yes	characteristic
387	#124	C₂³×C₁₉	1	1	yes	characteristic
388	#123	—	2	2	no	—
389	#123	—	2	1	no	—
390	#123	—	2	2	no	—
391	#123	—	2	1	no	—
392	#123	—	2	2	no	—
393	#123	—	2	2	no	—
394	#123	—	2	2	no	—
395	C₂²⋊Q₈	—	2	2	no	—
396	C₂²⋊Q₈	—	2	2	no	—
397	C₂²⋊Q₈	—	2	2	no	—
398	C₂²⋊Q₈	—	2	2	no	—
399	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
400	#121	—	2	2	no	—
401	#121	—	2	2	no	—
402	#121	—	2	2	no	—
403	#121	—	2	2	no	—
404	#121	—	2	2	no	—
405	#121	—	2	2	no	—
406	#121	—	2	2	no	—
407	#121	—	2	2	no	—
408	#121	D₄×C₁₉	1	2	yes	—
409	#120	—	2	1	no	—
410	#120	—	2	2	no	—
411	#120	—	2	1	no	—
412	#120	—	2	2	no	—
413	C₄×Q₈	D₄×C₁₉	1	2	yes	—
414	C₄×D₄	—	2	2	no	—
415	C₄×D₄	—	2	2	no	—
416	C₄×D₄	—	2	2	no	—
417	C₄×D₄	—	2	2	no	—
418	C₄×D₄	—	2	2	no	—
419	C₄×D₄	D₄×C₁₉	1	2	yes	—
420	#117	—	2	1	no	—
421	#117	—	2	2	no	—
422	C₂×C₄²	—	2	1	no	—
423	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
424	#107	—	2	2	no	—
425	#106	—	2	2	no	—
426	#103	—	2	2	no	—
427	#102	—	2	2	no	—
428	#102	—	2	2	no	—
429	#102	—	2	2	no	—
430	#97	—	2	1	no	—
431	#97	C₂³×C₁₉	1	2	yes	—
432	#97	C₂³×C₁₉	1	2	yes	—
433	#97	C₂³×C₁₉	1	1	yes	characteristic
434	#97	C₂³×C₁₉	1	1	yes	characteristic
435	C₄×C₈	—	2	2	no	—
436	C₁₉	#18984	1	1	yes	characteristic, direct product factor, Sylow
437	C₂⁴	—	2	1	no	—
438	#41	—	4	2	no	—
439	#41	—	4	2	no	—
440	#41	—	4	2	no	—
441	#41	—	4	2	no	—
442	#41	—	8	2	no	—
443	C₂×Q₈	—	2	1	no	—
444	C₂×Q₈	—	2	1	no	—
445	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
446	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
447	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
448	C₂×D₄	—	2	2	no	—
449	C₂×D₄	—	2	2	no	—
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	—	2	2	no	—
452	C₂×D₄	—	2	2	no	—
453	C₂×D₄	—	2	1	no	—
454	C₂×D₄	—	2	1	no	—
455	C₂×D₄	—	2	2	no	—
456	C₂×D₄	—	2	2	no	—
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	—	4	1	no	—
459	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
460	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
461	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	4	1	no	—
469	C₂²×C₄	—	8	2	no	—
470	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
471	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
472	Q₁₆	—	4	2	no	—
473	Q₁₆	—	4	2	no	—
474	SD₁₆	—	4	4	no	—
475	SD₁₆	—	4	2	no	—
476	SD₁₆	—	4	2	no	—
477	SD₁₆	—	4	2	no	—
478	SD₁₆	—	4	2	no	—
479	D₈	—	4	4	no	—
480	D₈	—	4	2	no	—
481	D₈	—	4	2	no	—
482	M₁₆	—	4	4	no	—
483	C₂×C₈	—	2	4	no	—
484	C₂×C₈	—	2	2	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	2	2	no	—
488	C₄⋊C₄	—	2	2	no	—
489	C₄⋊C₄	—	2	2	no	—
490	C₄⋊C₄	—	2	2	no	—
491	C₄⋊C₄	—	2	2	no	—
492	C₄⋊C₄	—	2	2	no	—
493	C₄⋊C₄	—	2	2	no	—
494	C₄⋊C₄	—	2	2	no	—
495	C₄⋊C₄	—	2	2	no	—
496	C₄⋊C₄	—	2	2	no	—
497	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
498	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
499	C₂²⋊C₄	—	2	1	no	—
500	C₂²⋊C₄	—	2	1	no	—
501	C₂²⋊C₄	—	2	2	no	—
502	C₂²⋊C₄	—	2	2	no	—
503	C₂²⋊C₄	—	2	2	no	—
504	C₂²⋊C₄	—	2	2	no	—
505	C₂²⋊C₄	—	2	2	no	—
506	C₂²⋊C₄	—	2	2	no	—
507	C₂²⋊C₄	—	2	2	no	—
508	C₂²⋊C₄	—	2	2	no	—
509	C₂²⋊C₄	—	2	2	no	—
510	C₂²⋊C₄	—	2	2	no	—
511	C₂²⋊C₄	—	2	2	no	—
512	C₂²⋊C₄	—	4	2	no	—
513	C₄²	—	2	1	no	—
514	C₄²	—	2	1	no	—
515	C₄²	—	2	2	no	—
516	C₄²	C₂×D₄×C₁₉	1	2	yes	—
517	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
518	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
519	C₂³	—	2	1	no	—
520	C₂³	—	2	2	no	—
521	C₂³	—	2	1	no	—
522	C₂³	—	4	1	no	—
523	C₂³	—	8	1	no	—
524	C₂³	—	8	2	no	—
525	C₂³	C₁₉×#120	1	1	yes	characteristic
526	Q₈	—	4	1	no	—
527	Q₈	—	4	1	no	—
528	Q₈	—	4	2	no	—
529	Q₈	—	4	1	no	—
530	Q₈	—	4	1	no	—
531	Q₈	—	8	1	no	—
532	D₄	—	4	1	no	—
533	D₄	—	4	1	no	—
534	D₄	—	4	2	no	—
535	D₄	—	4	1	no	—
536	D₄	—	4	1	no	—
537	D₄	—	4	2	no	—
538	D₄	—	4	2	no	—
539	D₄	—	8	2	no	—
540	D₄	—	8	1	no	—
541	D₄	—	8	1	no	—
542	D₄	—	8	2	no	—
543	D₄	—	8	2	no	—
544	D₄	—	8	1	no	—
545	D₄	—	8	2	no	—
546	D₄	—	8	2	no	—
547	D₄	—	8	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	4	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	8	2	no	—
560	C₂×C₄	—	8	1	no	—
561	C₂×C₄	—	8	2	no	—
562	C₂×C₄	—	8	2	no	—
563	C₂×C₄	C₁₉×#120	1	2	yes	—
564	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
565	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
566	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
567	C₈	—	2	2	no	—
568	C₈	—	2	2	no	—
569	C₈	—	2	4	no	—
570	C₈	—	4	2	no	—
571	C₂²	—	2	1	no	—
572	C₂²	—	2	2	no	—
573	C₂²	—	4	1	no	—
574	C₂²	—	4	2	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	4	2	no	—
577	C₂²	—	4	2	no	—
578	C₂²	—	4	2	no	—
579	C₂²	—	4	2	no	—
580	C₂²	—	8	4	no	—
581	C₂²	—	8	1	no	—
582	C₂²	—	8	2	no	—
583	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
584	C₄	—	2	1	no	—
585	C₄	—	2	2	no	—
586	C₄	—	2	2	no	—
587	C₄	—	4	1	no	—
588	C₄	—	4	2	no	—
589	C₄	—	4	1	no	—
590	C₄	—	4	2	no	—
591	C₄	—	4	2	no	—
592	C₄	—	8	1	no	—
593	C₄	C₁₉×#453	1	2	yes	—
594	C₂	—	4	1	no	—
595	C₂	—	8	1	no	—
596	C₂	—	8	2	no	—
597	C₂	—	8	1	no	—
598	C₂	—	16	1	no	—
599	C₂	C₂×C₁₉×#453	1	1	yes	characteristic
600	C₂	C₁₉×#3018	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₉	#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂×#120
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₁₉×#3529	C₂	semidirect
2. C₁₉×#3171	C₂	semidirect
3. C₁₉×#3150	C₂	semidirect
4. C₁₉×#1661	C₂	semidirect
5. C₁₉×#1660	C₂	semidirect
6. C₁₉×#1659	C₂	semidirect
7. C₁₉×#1657	C₂	semidirect
8. C₁₉×#1656	C₂	semidirect
9. C₁₉×#1655	C₂	semidirect
10. C₁₉×#1525	C₂	semidirect
11. C₁₉×#1524	C₂	semidirect
23. C₁₉×#532	C₂²	semidirect
28. C₁₉×#501	C₂²	semidirect
31. C₁₉×#497	C₂²	semidirect
35. C₁₉×#496	C₂²	semidirect
36. C₁₉×#490	C₂²	semidirect
42. C₄×M₁₆×C₁₉	C₂²	semidirect
43. C₂×C₁₉×#97	C₂²	semidirect
44. C₁₉×#330	C₂²	semidirect
45. C₁₉×#330	C₂²	semidirect
50. C₁₉×#329	C₂²	semidirect
218. #18984	C₁₉	direct (N × H)
271. #3529	C₂×C₁₉	semidirect
272. #3171	C₂×C₁₉	semidirect
273. #3150	C₂×C₁₉	semidirect
274. #1661	C₂×C₁₉	semidirect
275. #1660	C₂×C₁₉	semidirect
276. #1659	C₂×C₁₉	semidirect
277. #1657	C₂×C₁₉	semidirect
278. #1656	C₂×C₁₉	semidirect
279. #1655	C₂×C₁₉	semidirect
280. #1525	C₂×C₁₉	semidirect
281. #1524	C₂×C₁₉	semidirect
316. #532	C₂²×C₁₉	semidirect
321. #501	C₂²×C₁₉	semidirect
324. #497	C₂²×C₁₉	semidirect
328. #496	C₂²×C₁₉	semidirect
329. #490	C₂²×C₁₉	semidirect
335. C₄×M₁₆	C₂²×C₁₉	semidirect
336. C₂×#97	C₂²×C₁₉	semidirect
337. #330	C₂²×C₁₉	semidirect
338. #330	C₂²×C₁₉	semidirect
343. #329	C₂²×C₁₉	semidirect
436. C₁₉	#18984	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×#3529	2
C₁₉×#3171	2
C₁₉×#3150	2
C₁₉×#1661	2
C₁₉×#1660	2
C₁₉×#1659	2
C₁₉×#1657	2
C₁₉×#1656	2
C₁₉×#1655	2
C₁₉×#1525	2
C₁₉×#1524	2
#18984	19

Subgroups — C19×#18984 #18024943

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18984 #18024943