Subgroups — C₁₉×#19911 #18025870

Order 4864.

666 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3366	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3325	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3305	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3295	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1709	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1698	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1697	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1677	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1677	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1634	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1632	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1621	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1619	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1590	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×D₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#555	C₂²	1	1	yes	characteristic
17	C₁₉×#554	C₂²	1	1	yes	characteristic
18	C₁₉×#550	C₂²	1	1	yes	characteristic, complemented
19	D₄²×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#494	C₂²	1	1	yes	characteristic, complemented
21	C₁₉×#493	C₂²	1	1	yes	characteristic
22	C₁₉×#490	—	2	1	no	—
23	C₁₉×#486	C₂²	1	1	yes	characteristic
24	C₁₉×#486	C₂²	1	1	yes	characteristic
25	C₁₉×#486	C₂²	1	1	yes	characteristic, complemented
26	C₁₉×#486	C₂²	1	1	yes	characteristic, complemented
27	C₁₉×#482	—	2	1	no	—
28	C₁₉×#482	—	2	1	no	—
29	C₁₉×#481	—	2	1	no	—
30	C₁₉×#478	—	2	1	no	—
31	C₁₉×#477	C₂²	1	1	yes	characteristic, complemented
32	C₁₉×#476	C₂²	1	1	yes	characteristic
33	C₁₉×#476	C₂²	1	1	yes	characteristic
34	C₁₉×#476	C₂²	1	1	yes	characteristic, complemented
35	C₁₉×#469	—	2	1	no	—
36	C₁₉×#466	—	2	1	no	—
37	C₁₉×#465	—	2	1	no	—
38	C₁₉×#460	C₂²	1	1	yes	characteristic
39	C₁₉×#459	—	2	1	no	—
40	C₁₉×#459	C₂²	1	1	yes	characteristic
41	C₁₉×#459	C₂²	1	1	yes	characteristic
42	C₁₉×#459	C₂²	1	1	yes	characteristic
43	C₁₉×#450	—	2	1	no	—
44	C₁₉×#449	—	2	1	no	—
45	C₁₉×#447	—	2	1	no	—
46	C₁₉×#446	C₂²	1	1	yes	characteristic, complemented
47	C₁₉×#442	—	2	1	no	—
48	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
49	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
50	C₁₉×#436	C₂²	1	1	yes	characteristic
51	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
52	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
53	C₁₉×#418	—	2	1	no	—
54	C₁₉×#416	—	2	1	no	—
55	C₂×C₁₉×#102	—	2	1	no	—
56	C₁₉×#335	C₂²	1	1	yes	characteristic, complemented
57	C₁₉×#334	C₂²	1	1	yes	characteristic, complemented
58	C₁₉×#333	C₂²	1	1	yes	characteristic, complemented
59	C₁₉×#333	C₂²	1	1	yes	characteristic, complemented
60	C₁₉×#331	C₂²	1	1	yes	characteristic
61	C₁₉×#331	C₂²	1	1	yes	characteristic, complemented
62	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
63	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
64	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
65	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
66	C₈²×C₁₉	C₂²	1	1	yes	characteristic, complemented
67	C₂×#41×C₁₉	—	2	1	no	—
68	C₂²×D₄×C₁₉	—	2	1	no	—
69	C₂²×D₄×C₁₉	—	2	1	no	—
70	C₂×Q₁₆×C₁₉	—	4	1	no	—
71	C₂×SD₁₆×C₁₉	—	2	1	no	—
72	C₂×SD₁₆×C₁₉	D₄	1	1	yes	characteristic
73	C₂×D₈×C₁₉	—	2	1	no	—
74	C₂×D₈×C₁₉	—	2	1	no	—
75	C₂×D₈×C₁₉	—	2	1	no	—
76	C₂×D₈×C₁₉	—	4	1	no	—
77	C₂×D₈×C₁₉	D₄	1	1	yes	characteristic
78	C₂×M₁₆×C₁₉	—	2	1	no	—
79	C₂²×C₈×C₁₉	—	2	1	no	—
80	C₂²×C₈×C₁₉	—	2	1	no	—
81	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
82	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
83	C₁₉×#127	—	2	1	no	—
84	C₁₉×#127	C₂³	1	1	yes	characteristic
85	C₁₉×#127	C₂³	1	1	yes	characteristic
86	C₁₉×#125	—	2	1	no	—
87	C₁₉×#124	—	4	1	no	—
88	C₁₉×C₂²⋊Q₈	—	2	1	no	—
89	C₁₉×C₂²⋊Q₈	—	4	1	no	—
90	C₁₉×#121	—	2	1	no	—
91	C₁₉×#121	—	2	1	no	—
92	C₁₉×#121	—	2	1	no	—
93	C₁₉×#121	—	2	1	no	—
94	C₁₉×#121	—	2	1	no	—
95	C₁₉×#121	—	4	1	no	—
96	C₁₉×#120	—	4	1	no	—
97	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
98	C₄×D₄×C₁₉	—	2	1	no	—
99	C₄×D₄×C₁₉	—	2	1	no	—
100	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
101	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
102	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
103	C₁₉×#117	—	2	1	no	—
104	C₁₉×#117	—	2	1	no	—
105	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
106	C₁₉×#107	—	2	1	no	—
107	C₁₉×#107	D₄	1	1	yes	characteristic
108	C₁₉×#106	—	2	1	no	—
109	C₁₉×#106	—	2	1	no	—
110	C₁₉×#106	—	2	1	no	—
111	C₁₉×#106	D₄	1	1	yes	characteristic
112	C₁₉×C₄⋊C₈	—	2	1	no	—
113	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
114	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
115	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
116	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
117	C₁₉×#103	—	2	1	no	—
118	C₁₉×#103	D₄	1	1	yes	characteristic
119	C₁₉×#102	—	2	1	no	—
120	C₁₉×#102	—	2	1	no	—
121	C₁₉×#102	—	2	1	no	—
122	C₁₉×#102	—	2	1	no	—
123	C₁₉×#102	—	2	1	no	—
124	C₁₉×#102	—	2	1	no	—
125	C₁₉×#102	—	2	1	no	—
126	C₁₉×#102	—	2	1	no	—
127	C₁₉×#102	—	2	1	no	—
128	C₁₉×#102	—	2	1	no	—
129	C₁₉×#102	—	2	1	no	—
130	C₁₉×#102	—	2	1	no	—
131	C₁₉×#102	—	2	1	no	—
132	C₁₉×#102	—	2	1	no	—
133	C₁₉×#102	—	2	1	no	—
134	C₁₉×#102	D₄	1	1	yes	characteristic
135	C₁₉×#102	D₄	1	1	yes	characteristic
136	C₁₉×#102	D₄	1	1	yes	characteristic
137	C₁₉×C₂²⋊C₈	—	2	1	no	—
138	C₁₉×C₂²⋊C₈	—	2	1	no	—
139	C₁₉×C₂²⋊C₈	—	2	1	no	—
140	C₁₉×#97	—	2	1	no	—
141	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
142	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
144	C₂⁴×C₁₉	—	4	1	no	—
145	#41×C₁₉	—	4	2	no	—
146	#41×C₁₉	—	8	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×D₄×C₁₉	—	2	1	no	—
151	C₂×D₄×C₁₉	—	2	1	no	—
152	C₂×D₄×C₁₉	—	2	1	no	—
153	C₂×D₄×C₁₉	—	2	1	no	—
154	C₂×D₄×C₁₉	—	2	1	no	—
155	C₂×D₄×C₁₉	—	2	1	no	—
156	C₂×D₄×C₁₉	—	4	1	no	—
157	C₂×D₄×C₁₉	—	4	1	no	—
158	C₂×D₄×C₁₉	—	4	1	no	—
159	C₂×D₄×C₁₉	—	4	1	no	—
160	C₂×D₄×C₁₉	—	4	2	no	—
161	C₂×D₄×C₁₉	—	4	2	no	—
162	C₂×D₄×C₁₉	—	4	1	no	—
163	C₂×D₄×C₁₉	—	8	1	no	—
164	C₂×D₄×C₁₉	—	8	1	no	—
165	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
166	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
167	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₉	—	2	1	no	—
169	C₂²×C₄×C₁₉	—	2	1	no	—
170	C₂²×C₄×C₁₉	—	2	1	no	—
171	C₂²×C₄×C₁₉	—	4	1	no	—
172	C₂²×C₄×C₁₉	—	4	1	no	—
173	Q₁₆×C₁₉	—	8	2	no	—
174	SD₁₆×C₁₉	—	4	1	no	—
175	SD₁₆×C₁₉	—	8	1	no	—
176	D₈×C₁₉	—	2	2	no	—
177	D₈×C₁₉	—	4	2	no	—
178	D₈×C₁₉	—	8	2	no	—
179	D₈×C₁₉	—	8	1	no	—
180	D₈×C₁₉	—	8	1	no	—
181	M₁₆×C₁₉	—	8	1	no	—
182	C₂×C₈×C₁₉	—	2	1	no	—
183	C₂×C₈×C₁₉	—	2	1	no	—
184	C₂×C₈×C₁₉	—	2	1	no	—
185	C₂×C₈×C₁₉	—	2	1	no	—
186	C₂×C₈×C₁₉	—	2	1	no	—
187	C₂×C₈×C₁₉	—	8	1	no	—
188	C₂×C₈×C₁₉	—	8	1	no	—
189	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
190	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
191	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
192	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
193	C₄⋊C₄×C₁₉	—	2	1	no	—
194	C₄⋊C₄×C₁₉	—	2	1	no	—
195	C₄⋊C₄×C₁₉	—	2	1	no	—
196	C₄⋊C₄×C₁₉	—	2	1	no	—
197	C₄⋊C₄×C₁₉	—	2	1	no	—
198	C₄⋊C₄×C₁₉	—	4	1	no	—
199	C₄⋊C₄×C₁₉	—	4	1	no	—
200	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
201	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
202	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
203	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
204	C₂²⋊C₄×C₁₉	—	2	1	no	—
205	C₂²⋊C₄×C₁₉	—	2	1	no	—
206	C₂²⋊C₄×C₁₉	—	2	1	no	—
207	C₂²⋊C₄×C₁₉	—	4	1	no	—
208	C₂²⋊C₄×C₁₉	—	4	1	no	—
209	C₂²⋊C₄×C₁₉	—	4	1	no	—
210	C₂²⋊C₄×C₁₉	—	4	1	no	—
211	C₂²⋊C₄×C₁₉	—	4	1	no	—
212	C₄²×C₁₉	—	2	1	no	—
213	C₄²×C₁₉	—	4	1	no	—
214	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
215	#19911	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
216	C₂³×C₁₉	—	2	1	no	—
217	C₂³×C₁₉	—	2	1	no	—
218	C₂³×C₁₉	—	2	1	no	—
219	C₂³×C₁₉	—	4	1	no	—
220	C₂³×C₁₉	—	4	1	no	—
221	C₂³×C₁₉	—	8	2	no	—
222	C₂³×C₁₉	—	8	2	no	—
223	C₂³×C₁₉	—	16	1	no	—
224	Q₈×C₁₉	—	2	1	no	—
225	Q₈×C₁₉	—	2	1	no	—
226	Q₈×C₁₉	—	8	1	no	—
227	Q₈×C₁₉	—	8	1	no	—
228	D₄×C₁₉	—	2	1	no	—
229	D₄×C₁₉	—	2	1	no	—
230	D₄×C₁₉	—	2	1	no	—
231	D₄×C₁₉	—	2	1	no	—
232	D₄×C₁₉	—	2	1	no	—
233	D₄×C₁₉	—	4	1	no	—
234	D₄×C₁₉	—	4	1	no	—
235	D₄×C₁₉	—	4	1	no	—
236	D₄×C₁₉	—	4	1	no	—
237	D₄×C₁₉	—	4	1	no	—
238	D₄×C₁₉	—	4	1	no	—
239	D₄×C₁₉	—	4	1	no	—
240	D₄×C₁₉	—	4	1	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	—	16	1	no	—
247	D₄×C₁₉	—	16	1	no	—
248	D₄×C₁₉	#135	1	2	yes	—
249	C₂×C₄×C₁₉	—	2	1	no	—
250	C₂×C₄×C₁₉	—	2	1	no	—
251	C₂×C₄×C₁₉	—	2	1	no	—
252	C₂×C₄×C₁₉	—	2	1	no	—
253	C₂×C₄×C₁₉	—	2	1	no	—
254	C₂×C₄×C₁₉	—	4	1	no	—
255	C₂×C₄×C₁₉	—	4	1	no	—
256	C₂×C₄×C₁₉	—	4	1	no	—
257	C₂×C₄×C₁₉	—	4	1	no	—
258	C₂×C₄×C₁₉	—	4	1	no	—
259	C₂×C₄×C₁₉	—	4	1	no	—
260	C₂×C₄×C₁₉	—	4	1	no	—
261	C₂×C₄×C₁₉	—	4	1	no	—
262	C₂×C₄×C₁₉	—	8	2	no	—
263	C₂×C₄×C₁₉	—	16	1	no	—
264	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
265	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
266	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
267	C₈×C₁₉	—	2	2	no	—
268	C₈×C₁₉	—	2	1	no	—
269	C₈×C₁₉	—	2	1	no	—
270	C₈×C₁₉	—	2	1	no	—
271	C₈×C₁₉	—	2	1	no	—
272	C₈×C₁₉	—	4	1	no	—
273	C₈×C₁₉	—	4	1	no	—
274	C₈×C₁₉	—	4	1	no	—
275	C₈×C₁₉	—	4	1	no	—
276	#3366	C₂×C₁₉	1	1	yes	characteristic, complemented
277	#3325	C₂×C₁₉	1	1	yes	characteristic, complemented
278	#3305	C₂×C₁₉	1	1	yes	characteristic, complemented
279	#3295	C₂×C₁₉	1	1	yes	characteristic, complemented
280	#1709	C₂×C₁₉	1	1	yes	characteristic, complemented
281	#1698	C₂×C₁₉	1	1	yes	characteristic, complemented
282	#1697	C₂×C₁₉	1	1	yes	characteristic, complemented
283	#1677	C₂×C₁₉	1	1	yes	characteristic, complemented
284	#1677	C₂×C₁₉	1	1	yes	characteristic, complemented
285	#1634	C₂×C₁₉	1	1	yes	characteristic, complemented
286	#1632	C₂×C₁₉	1	1	yes	characteristic, complemented
287	#1621	C₂×C₁₉	1	1	yes	characteristic, complemented
288	#1619	C₂×C₁₉	1	1	yes	characteristic, complemented
289	#1590	C₂×C₁₉	1	1	yes	characteristic, complemented
290	C₈×D₈	C₂×C₁₉	1	1	yes	characteristic, complemented
291	C₂²×C₁₉	—	2	2	no	—
292	C₂²×C₁₉	—	4	1	no	—
293	C₂²×C₁₉	—	4	1	no	—
294	C₂²×C₁₉	—	4	1	no	—
295	C₂²×C₁₉	—	4	1	no	—
296	C₂²×C₁₉	—	4	1	no	—
297	C₂²×C₁₉	—	4	1	no	—
298	C₂²×C₁₉	—	4	1	no	—
299	C₂²×C₁₉	—	4	1	no	—
300	C₂²×C₁₉	—	8	1	no	—
301	C₂²×C₁₉	—	8	1	no	—
302	C₂²×C₁₉	—	8	1	no	—
303	C₂²×C₁₉	—	8	1	no	—
304	C₂²×C₁₉	—	8	1	no	—
305	C₂²×C₁₉	—	8	1	no	—
306	C₂²×C₁₉	—	16	4	no	—
307	C₂²×C₁₉	D₄²	1	1	yes	characteristic
308	C₄×C₁₉	—	2	1	no	—
309	C₄×C₁₉	—	4	1	no	—
310	C₄×C₁₉	—	4	1	no	—
311	C₄×C₁₉	—	4	1	no	—
312	C₄×C₁₉	—	4	1	no	—
313	C₄×C₁₉	—	4	1	no	—
314	C₄×C₁₉	—	8	1	no	—
315	C₄×C₁₉	—	8	1	no	—
316	C₄×C₁₉	C₂×#135	1	1	yes	characteristic
317	C₄×C₁₉	#575	1	1	yes	characteristic
318	C₄×C₁₉	#576	1	1	yes	characteristic
319	C₄×C₁₉	#577	1	1	yes	characteristic
320	#555	C₂²×C₁₉	1	1	yes	characteristic
321	#554	C₂²×C₁₉	1	1	yes	characteristic
322	#550	C₂²×C₁₉	1	1	yes	characteristic, complemented
323	D₄²	C₂²×C₁₉	1	1	yes	characteristic
324	#494	C₂²×C₁₉	1	1	yes	characteristic, complemented
325	#493	C₂²×C₁₉	1	1	yes	characteristic
326	#490	—	2	1	no	—
327	#486	C₂²×C₁₉	1	1	yes	characteristic
328	#486	C₂²×C₁₉	1	1	yes	characteristic
329	#486	C₂²×C₁₉	1	1	yes	characteristic, complemented
330	#486	C₂²×C₁₉	1	1	yes	characteristic, complemented
331	#482	—	2	1	no	—
332	#482	—	2	1	no	—
333	#481	—	2	1	no	—
334	#478	—	2	1	no	—
335	#477	C₂²×C₁₉	1	1	yes	characteristic, complemented
336	#476	C₂²×C₁₉	1	1	yes	characteristic
337	#476	C₂²×C₁₉	1	1	yes	characteristic
338	#476	C₂²×C₁₉	1	1	yes	characteristic, complemented
339	#469	—	2	1	no	—
340	#466	—	2	1	no	—
341	#465	—	2	1	no	—
342	#460	C₂²×C₁₉	1	1	yes	characteristic
343	#459	—	2	1	no	—
344	#459	C₂²×C₁₉	1	1	yes	characteristic
345	#459	C₂²×C₁₉	1	1	yes	characteristic
346	#459	C₂²×C₁₉	1	1	yes	characteristic
347	#450	—	2	1	no	—
348	#449	—	2	1	no	—
349	#447	—	2	1	no	—
350	#446	C₂²×C₁₉	1	1	yes	characteristic, complemented
351	#442	—	2	1	no	—
352	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
353	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
354	#436	C₂²×C₁₉	1	1	yes	characteristic
355	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
356	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
357	#418	—	2	1	no	—
358	#416	—	2	1	no	—
359	C₂×#102	—	2	1	no	—
360	#335	C₂²×C₁₉	1	1	yes	characteristic, complemented
361	#334	C₂²×C₁₉	1	1	yes	characteristic, complemented
362	#333	C₂²×C₁₉	1	1	yes	characteristic, complemented
363	#333	C₂²×C₁₉	1	1	yes	characteristic, complemented
364	#331	C₂²×C₁₉	1	1	yes	characteristic
365	#331	C₂²×C₁₉	1	1	yes	characteristic, complemented
366	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
367	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
368	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
369	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
370	C₈²	C₂²×C₁₉	1	1	yes	characteristic, complemented
371	C₂×C₁₉	—	4	2	no	—
372	C₂×C₁₉	—	8	1	no	—
373	C₂×C₁₉	—	8	1	no	—
374	C₂×C₁₉	—	16	1	no	—
375	C₂×C₁₉	—	16	1	no	—
376	C₂×C₁₉	#3273	1	1	yes	characteristic
377	C₂×C₁₉	#3282	1	1	yes	characteristic
378	C₂×C₁₉	#3292	1	1	yes	characteristic
379	C₂×#41	—	2	1	no	—
380	C₂²×D₄	—	2	1	no	—
381	C₂²×D₄	—	2	1	no	—
382	C₂×Q₁₆	—	4	1	no	—
383	C₂×SD₁₆	—	2	1	no	—
384	C₂×SD₁₆	D₄×C₁₉	1	1	yes	characteristic
385	C₂×D₈	—	2	1	no	—
386	C₂×D₈	—	2	1	no	—
387	C₂×D₈	—	2	1	no	—
388	C₂×D₈	—	4	1	no	—
389	C₂×D₈	D₄×C₁₉	1	1	yes	characteristic
390	C₂×M₁₆	—	2	1	no	—
391	C₂²×C₈	—	2	1	no	—
392	C₂²×C₈	—	2	1	no	—
393	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
394	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
395	#127	—	2	1	no	—
396	#127	C₂³×C₁₉	1	1	yes	characteristic
397	#127	C₂³×C₁₉	1	1	yes	characteristic
398	#125	—	2	1	no	—
399	#124	—	4	1	no	—
400	C₂²⋊Q₈	—	2	1	no	—
401	C₂²⋊Q₈	—	4	1	no	—
402	#121	—	2	1	no	—
403	#121	—	2	1	no	—
404	#121	—	2	1	no	—
405	#121	—	2	1	no	—
406	#121	—	2	1	no	—
407	#121	—	4	1	no	—
408	#120	—	4	1	no	—
409	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
410	C₄×D₄	—	2	1	no	—
411	C₄×D₄	—	2	1	no	—
412	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
413	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
414	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
415	#117	—	2	1	no	—
416	#117	—	2	1	no	—
417	C₂×C₄⋊C₄	—	2	1	no	—
418	#107	—	2	1	no	—
419	#107	D₄×C₁₉	1	1	yes	characteristic
420	#106	—	2	1	no	—
421	#106	—	2	1	no	—
422	#106	—	2	1	no	—
423	#106	D₄×C₁₉	1	1	yes	characteristic
424	C₄⋊C₈	—	2	1	no	—
425	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
426	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
427	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
428	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
429	#103	—	2	1	no	—
430	#103	D₄×C₁₉	1	1	yes	characteristic
431	#102	—	2	1	no	—
432	#102	—	2	1	no	—
433	#102	—	2	1	no	—
434	#102	—	2	1	no	—
435	#102	—	2	1	no	—
436	#102	—	2	1	no	—
437	#102	—	2	1	no	—
438	#102	—	2	1	no	—
439	#102	—	2	1	no	—
440	#102	—	2	1	no	—
441	#102	—	2	1	no	—
442	#102	—	2	1	no	—
443	#102	—	2	1	no	—
444	#102	—	2	1	no	—
445	#102	—	2	1	no	—
446	#102	D₄×C₁₉	1	1	yes	characteristic
447	#102	D₄×C₁₉	1	1	yes	characteristic
448	#102	D₄×C₁₉	1	1	yes	characteristic
449	C₂²⋊C₈	—	2	1	no	—
450	C₂²⋊C₈	—	2	1	no	—
451	C₂²⋊C₈	—	2	1	no	—
452	#97	—	2	1	no	—
453	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
454	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
455	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
456	C₁₉	#19911	1	1	yes	characteristic, direct product factor, Sylow
457	C₂⁴	—	4	1	no	—
458	#41	—	4	2	no	—
459	#41	—	8	1	no	—
460	C₂×Q₈	—	2	1	no	—
461	C₂×Q₈	—	2	1	no	—
462	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
463	C₂×D₄	—	2	1	no	—
464	C₂×D₄	—	2	1	no	—
465	C₂×D₄	—	2	1	no	—
466	C₂×D₄	—	2	1	no	—
467	C₂×D₄	—	2	1	no	—
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	—	4	1	no	—
470	C₂×D₄	—	4	1	no	—
471	C₂×D₄	—	4	1	no	—
472	C₂×D₄	—	4	1	no	—
473	C₂×D₄	—	4	2	no	—
474	C₂×D₄	—	4	2	no	—
475	C₂×D₄	—	4	1	no	—
476	C₂×D₄	—	8	1	no	—
477	C₂×D₄	—	8	1	no	—
478	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
479	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
480	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
481	C₂²×C₄	—	2	1	no	—
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	4	1	no	—
485	C₂²×C₄	—	4	1	no	—
486	Q₁₆	—	8	2	no	—
487	SD₁₆	—	4	1	no	—
488	SD₁₆	—	8	1	no	—
489	D₈	—	2	2	no	—
490	D₈	—	4	2	no	—
491	D₈	—	8	2	no	—
492	D₈	—	8	1	no	—
493	D₈	—	8	1	no	—
494	M₁₆	—	8	1	no	—
495	C₂×C₈	—	2	1	no	—
496	C₂×C₈	—	2	1	no	—
497	C₂×C₈	—	2	1	no	—
498	C₂×C₈	—	2	1	no	—
499	C₂×C₈	—	2	1	no	—
500	C₂×C₈	—	8	1	no	—
501	C₂×C₈	—	8	1	no	—
502	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
503	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
504	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
505	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	2	1	no	—
508	C₄⋊C₄	—	2	1	no	—
509	C₄⋊C₄	—	2	1	no	—
510	C₄⋊C₄	—	2	1	no	—
511	C₄⋊C₄	—	4	1	no	—
512	C₄⋊C₄	—	4	1	no	—
513	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
514	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
515	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
516	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
517	C₂²⋊C₄	—	2	1	no	—
518	C₂²⋊C₄	—	2	1	no	—
519	C₂²⋊C₄	—	2	1	no	—
520	C₂²⋊C₄	—	4	1	no	—
521	C₂²⋊C₄	—	4	1	no	—
522	C₂²⋊C₄	—	4	1	no	—
523	C₂²⋊C₄	—	4	1	no	—
524	C₂²⋊C₄	—	4	1	no	—
525	C₄²	—	2	1	no	—
526	C₄²	—	4	1	no	—
527	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
528	C₂³	—	2	1	no	—
529	C₂³	—	2	1	no	—
530	C₂³	—	2	1	no	—
531	C₂³	—	4	1	no	—
532	C₂³	—	4	1	no	—
533	C₂³	—	8	2	no	—
534	C₂³	—	8	2	no	—
535	C₂³	—	16	1	no	—
536	Q₈	—	2	1	no	—
537	Q₈	—	2	1	no	—
538	Q₈	—	8	1	no	—
539	Q₈	—	8	1	no	—
540	D₄	—	2	1	no	—
541	D₄	—	2	1	no	—
542	D₄	—	2	1	no	—
543	D₄	—	2	1	no	—
544	D₄	—	2	1	no	—
545	D₄	—	4	1	no	—
546	D₄	—	4	1	no	—
547	D₄	—	4	1	no	—
548	D₄	—	4	1	no	—
549	D₄	—	4	1	no	—
550	D₄	—	4	1	no	—
551	D₄	—	4	1	no	—
552	D₄	—	4	1	no	—
553	D₄	—	8	1	no	—
554	D₄	—	8	1	no	—
555	D₄	—	8	2	no	—
556	D₄	—	8	2	no	—
557	D₄	—	8	2	no	—
558	D₄	—	16	1	no	—
559	D₄	—	16	1	no	—
560	D₄	C₁₉×#135	1	2	yes	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	8	2	no	—
575	C₂×C₄	—	16	1	no	—
576	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
577	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
578	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
579	C₈	—	2	2	no	—
580	C₈	—	2	1	no	—
581	C₈	—	2	1	no	—
582	C₈	—	2	1	no	—
583	C₈	—	2	1	no	—
584	C₈	—	4	1	no	—
585	C₈	—	4	1	no	—
586	C₈	—	4	1	no	—
587	C₈	—	4	1	no	—
588	C₂²	—	2	2	no	—
589	C₂²	—	4	1	no	—
590	C₂²	—	4	1	no	—
591	C₂²	—	4	1	no	—
592	C₂²	—	4	1	no	—
593	C₂²	—	4	1	no	—
594	C₂²	—	4	1	no	—
595	C₂²	—	4	1	no	—
596	C₂²	—	4	1	no	—
597	C₂²	—	8	1	no	—
598	C₂²	—	8	1	no	—
599	C₂²	—	8	1	no	—
600	C₂²	—	8	1	no	—
601	C₂²	—	8	1	no	—
602	C₂²	—	8	1	no	—
603	C₂²	—	16	4	no	—
604	C₂²	D₄²×C₁₉	1	1	yes	characteristic
605	C₄	—	2	1	no	—
606	C₄	—	4	1	no	—
607	C₄	—	4	1	no	—
608	C₄	—	4	1	no	—
609	C₄	—	4	1	no	—
610	C₄	—	4	1	no	—
611	C₄	—	8	1	no	—
612	C₄	—	8	1	no	—
613	C₄	C₂×C₁₉×#135	1	1	yes	characteristic
614	C₄	C₁₉×#575	1	1	yes	characteristic
615	C₄	C₁₉×#576	1	1	yes	characteristic
616	C₄	C₁₉×#577	1	1	yes	characteristic
617	C₂	—	4	2	no	—
618	C₂	—	8	1	no	—
619	C₂	—	8	1	no	—
620	C₂	—	16	1	no	—
621	C₂	—	16	1	no	—
622	C₂	C₁₉×#3273	1	1	yes	characteristic
623	C₂	C₁₉×#3282	1	1	yes	characteristic
624	C₂	C₁₉×#3292	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3366	C₂	semidirect
2. C₁₉×#3325	C₂	semidirect
3. C₁₉×#3305	C₂	semidirect
4. C₁₉×#3295	C₂	semidirect
5. C₁₉×#1709	C₂	semidirect
6. C₁₉×#1698	C₂	semidirect
7. C₁₉×#1697	C₂	semidirect
8. C₁₉×#1677	C₂	semidirect
9. C₁₉×#1677	C₂	semidirect
10. C₁₉×#1634	C₂	semidirect
11. C₁₉×#1632	C₂	semidirect
12. C₁₉×#1621	C₂	semidirect
13. C₁₉×#1619	C₂	semidirect
14. C₁₉×#1590	C₂	semidirect
15. C₈×D₈×C₁₉	C₂	semidirect
18. C₁₉×#550	C₂²	semidirect
20. C₁₉×#494	C₂²	semidirect
25. C₁₉×#486	C₂²	semidirect
26. C₁₉×#486	C₂²	semidirect
31. C₁₉×#477	C₂²	semidirect
34. C₁₉×#476	C₂²	semidirect
46. C₁₉×#446	C₂²	semidirect
52. C₈×D₄×C₁₉	C₂²	semidirect
56. C₁₉×#335	C₂²	semidirect
57. C₁₉×#334	C₂²	semidirect
58. C₁₉×#333	C₂²	semidirect
59. C₁₉×#333	C₂²	semidirect
61. C₁₉×#331	C₂²	semidirect
62. C₁₉×Q₈⋊C₈	C₂²	semidirect
65. C₁₉×D₄⋊C₈	C₂²	semidirect
66. C₈²×C₁₉	C₂²	semidirect
215. #19911	C₁₉	direct (N × H)
276. #3366	C₂×C₁₉	semidirect
277. #3325	C₂×C₁₉	semidirect
278. #3305	C₂×C₁₉	semidirect
279. #3295	C₂×C₁₉	semidirect
280. #1709	C₂×C₁₉	semidirect
281. #1698	C₂×C₁₉	semidirect
282. #1697	C₂×C₁₉	semidirect
283. #1677	C₂×C₁₉	semidirect
284. #1677	C₂×C₁₉	semidirect
285. #1634	C₂×C₁₉	semidirect
286. #1632	C₂×C₁₉	semidirect
287. #1621	C₂×C₁₉	semidirect
288. #1619	C₂×C₁₉	semidirect
289. #1590	C₂×C₁₉	semidirect
290. C₈×D₈	C₂×C₁₉	semidirect
322. #550	C₂²×C₁₉	semidirect
324. #494	C₂²×C₁₉	semidirect
329. #486	C₂²×C₁₉	semidirect
330. #486	C₂²×C₁₉	semidirect
335. #477	C₂²×C₁₉	semidirect
338. #476	C₂²×C₁₉	semidirect
350. #446	C₂²×C₁₉	semidirect
356. C₈×D₄	C₂²×C₁₉	semidirect
360. #335	C₂²×C₁₉	semidirect
361. #334	C₂²×C₁₉	semidirect
362. #333	C₂²×C₁₉	semidirect
363. #333	C₂²×C₁₉	semidirect
365. #331	C₂²×C₁₉	semidirect
366. Q₈⋊C₈	C₂²×C₁₉	semidirect
369. D₄⋊C₈	C₂²×C₁₉	semidirect
370. C₈²	C₂²×C₁₉	semidirect
456. C₁₉	#19911	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×#3366	2
C₁₉×#3325	2
C₁₉×#3305	2
C₁₉×#3295	2
C₁₉×#1709	2
C₁₉×#1698	2
C₁₉×#1697	2
C₁₉×#1677	2
C₁₉×#1634	2
C₁₉×#1632	2
C₁₉×#1621	2
C₁₉×#1619	2
C₁₉×#1590	2
C₈×D₈×C₁₉	2
#19911	19

Subgroups — C19×#19911 #18025870

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19911 #18025870