Subgroups — C₁₉×#33555 #18039514

Order 4864.

1146 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3540	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3027	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3025	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3022	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2199	C₂	1	4	yes	maximal, complemented
6	C₁₉×#2197	C₂	1	4	yes	maximal, complemented
7	C₁₉×#2129	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2122	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2120	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#585	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×#137	—	2	1	no	—
12	C₁₉×H(3,𝔽₄)	C₂²	1	2	yes	complemented
13	C₁₉×#560	—	2	1	no	—
14	C₁₉×#559	—	2	1	no	—
15	C₁₉×#556	—	2	1	no	—
16	C₁₉×#555	—	2	1	no	—
17	C₁₉×#551	C₂²	1	2	yes	complemented
18	C₁₉×#548	—	2	1	no	—
19	C₁₉×#546	—	2	1	no	—
20	C₁₉×#542	—	2	2	no	—
21	C₁₉×#542	—	2	1	no	—
22	C₁₉×#538	—	2	2	no	—
23	C₁₉×#536	C₂²	1	1	yes	characteristic
24	C₁₉×#535	—	2	1	no	—
25	C₁₉×#535	C₂²	1	1	yes	characteristic
26	C₁₉×#525	—	2	1	no	—
27	C₁₉×#525	—	2	1	no	—
28	C₁₉×#525	C₂²	1	1	yes	characteristic
29	C₁₉×#458	—	2	1	no	—
30	C₁₉×#458	C₂²	1	2	yes	—
31	C₁₉×B(4,𝔽₂)	—	2	1	no	—
32	C₁₉×B(4,𝔽₂)	—	2	2	no	—
33	C₁₉×B(4,𝔽₂)	C₂²	1	4	yes	—
34	C₁₉×B(4,𝔽₂)	C₂²	1	2	yes	—
35	C₁₉×#456	—	2	2	no	—
36	C₁₉×#455	C₂²	1	4	yes	—
37	C₁₉×#421	—	2	1	no	—
38	C₁₉×#413	C₂²	1	1	yes	characteristic
39	C₁₉×#410	—	2	1	no	—
40	C₁₉×#410	—	2	1	no	—
41	C₁₉×#410	C₂²	1	1	yes	characteristic
42	C₁₉×#410	C₂²	1	1	yes	characteristic
43	C₁₉×#354	C₂²	1	4	yes	complemented
44	C₁₉×#352	C₂²	1	2	yes	complemented
45	C₁₉×AΣL(1,𝔽₁₆)	C₂²	1	4	yes	complemented
46	C₁₉×AΣL(1,𝔽₁₆)	C₂²	1	2	yes	complemented
47	C₁₉×2₋¹⁺⁴	—	2	1	no	—
48	C₁₉×2₋¹⁺⁴	—	4	1	no	—
49	C₁₉×H(5,𝔽₂)	—	2	1	no	—
50	C₁₉×H(5,𝔽₂)	—	2	1	no	—
51	C₁₉×H(5,𝔽₂)	—	4	1	no	—
52	C₁₉×H(5,𝔽₂)	C₂³	1	2	yes	—
53	C₂×#41×C₁₉	—	2	1	no	—
54	C₂×#41×C₁₉	—	2	1	no	—
55	C₂×#41×C₁₉	—	2	1	no	—
56	C₂×#41×C₁₉	—	2	1	no	—
57	C₂×#41×C₁₉	—	4	2	no	—
58	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
59	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic, complemented
60	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic, complemented
61	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic, complemented
62	C₁₉×#137	—	2	4	no	—
63	C₁₉×#137	—	4	2	no	—
64	C₂×Q₁₆×C₁₉	—	4	1	no	—
65	C₂×SD₁₆×C₁₉	—	4	1	no	—
66	C₂×M₁₆×C₁₉	—	2	1	no	—
67	C₁₉×C₄⋊Q₈	—	2	1	no	—
68	C₁₉×C₄⋊Q₈	D₄	1	2	yes	complemented
69	C₁₉×#127	—	2	1	no	—
70	C₁₉×#127	—	4	1	no	—
71	C₁₉×#126	—	2	2	no	—
72	C₁₉×#126	—	2	2	no	—
73	C₁₉×#126	—	2	2	no	—
74	C₁₉×#124	—	2	2	no	—
75	C₁₉×#124	—	2	1	no	—
76	C₁₉×#124	—	2	1	no	—
77	C₁₉×#124	—	2	2	no	—
78	C₁₉×#124	—	2	2	no	—
79	C₁₉×#124	—	2	2	no	—
80	C₁₉×#124	—	2	2	no	—
81	C₁₉×#124	—	4	1	no	—
82	C₁₉×#124	C₂³	1	2	yes	—
83	C₁₉×#123	—	2	2	no	—
84	C₁₉×#123	—	2	2	no	—
85	C₁₉×#123	—	2	1	no	—
86	C₁₉×#123	—	2	1	no	—
87	C₁₉×#123	—	2	2	no	—
88	C₁₉×#123	—	2	2	no	—
89	C₁₉×#123	D₄	1	1	yes	characteristic, complemented
90	C₁₉×#123	C₂³	1	1	yes	characteristic
91	C₁₉×C₂²⋊Q₈	—	2	1	no	—
92	C₁₉×C₂²⋊Q₈	—	2	2	no	—
93	C₁₉×C₂²⋊Q₈	—	2	1	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	—	4	1	no	—
98	C₁₉×#121	—	2	1	no	—
99	C₁₉×#121	—	2	2	no	—
100	C₁₉×#121	—	2	2	no	—
101	C₁₉×#121	—	2	2	no	—
102	C₁₉×#121	—	2	1	no	—
103	C₁₉×#121	—	2	1	no	—
104	C₁₉×#121	—	2	1	no	—
105	C₁₉×#121	—	4	2	no	—
106	C₁₉×#121	—	4	1	no	—
107	C₁₉×#120	—	2	2	no	—
108	C₁₉×#120	—	2	2	no	—
109	C₁₉×#120	—	2	2	no	—
110	C₁₉×#120	—	2	4	no	—
111	C₁₉×#120	D₄	1	1	yes	characteristic, complemented
112	C₁₉×#120	D₄	1	2	yes	complemented
113	C₁₉×#120	C₂³	1	1	yes	characteristic
114	C₁₉×#120	C₂³	1	2	yes	—
115	C₄×Q₈×C₁₉	—	2	1	no	—
116	C₄×Q₈×C₁₉	—	2	2	no	—
117	C₄×D₄×C₁₉	—	2	2	no	—
118	C₄×D₄×C₁₉	—	2	2	no	—
119	C₄×D₄×C₁₉	—	2	1	no	—
120	C₄×D₄×C₁₉	—	2	2	no	—
121	C₄×D₄×C₁₉	—	2	1	no	—
122	C₄×D₄×C₁₉	—	2	1	no	—
123	C₄×D₄×C₁₉	—	4	2	no	—
124	C₁₉×#117	—	2	1	no	—
125	C₁₉×#117	—	2	2	no	—
126	C₁₉×#117	—	2	1	no	—
127	C₁₉×#117	—	2	1	no	—
128	C₁₉×#117	D₄	1	1	yes	characteristic, complemented
129	C₁₉×#117	D₄	1	1	yes	characteristic, complemented
130	C₁₉×#117	D₄	1	1	yes	characteristic, complemented
131	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
132	C₁₉×#104	—	2	4	no	—
133	C₁₉×#101	—	2	1	no	—
134	C₁₉×#100	C₂³	1	2	yes	—
135	C₁₉×#99	—	2	1	no	—
136	C₁₉×#99	—	2	1	no	—
137	C₁₉×#99	—	2	4	no	—
138	C₁₉×#99	—	2	2	no	—
139	C₁₉×#99	—	2	2	no	—
140	C₁₉×#99	C₂³	1	2	yes	—
141	C₁₉×#99	C₂³	1	2	yes	—
142	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
143	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
144	#41×C₁₉	—	2	2	no	—
145	#41×C₁₉	—	2	2	no	—
146	#41×C₁₉	—	4	1	no	—
147	#41×C₁₉	—	4	1	no	—
148	#41×C₁₉	—	4	2	no	—
149	#41×C₁₉	—	4	1	no	—
150	#41×C₁₉	—	4	1	no	—
151	#41×C₁₉	—	4	1	no	—
152	#41×C₁₉	—	4	1	no	—
153	#41×C₁₉	—	4	1	no	—
154	#41×C₁₉	—	4	2	no	—
155	#41×C₁₉	—	4	2	no	—
156	#41×C₁₉	—	4	2	no	—
157	#41×C₁₉	—	4	1	no	—
158	#41×C₁₉	—	4	1	no	—
159	#41×C₁₉	—	4	1	no	—
160	#41×C₁₉	—	8	1	no	—
161	#41×C₁₉	—	8	1	no	—
162	C₂×Q₈×C₁₉	—	2	1	no	—
163	C₂×Q₈×C₁₉	—	2	1	no	—
164	C₂×Q₈×C₁₉	—	2	2	no	—
165	C₂×Q₈×C₁₉	—	2	1	no	—
166	C₂×Q₈×C₁₉	—	2	1	no	—
167	C₂×Q₈×C₁₉	—	4	1	no	—
168	C₂×Q₈×C₁₉	—	4	1	no	—
169	C₂×Q₈×C₁₉	—	4	2	no	—
170	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
171	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
172	C₂×D₄×C₁₉	—	2	1	no	—
173	C₂×D₄×C₁₉	—	2	1	no	—
174	C₂×D₄×C₁₉	—	2	1	no	—
175	C₂×D₄×C₁₉	—	2	2	no	—
176	C₂×D₄×C₁₉	—	2	2	no	—
177	C₂×D₄×C₁₉	—	2	2	no	—
178	C₂×D₄×C₁₉	—	2	2	no	—
179	C₂×D₄×C₁₉	—	2	1	no	—
180	C₂×D₄×C₁₉	—	2	2	no	—
181	C₂×D₄×C₁₉	—	2	1	no	—
182	C₂×D₄×C₁₉	—	2	2	no	—
183	C₂×D₄×C₁₉	—	2	1	no	—
184	C₂×D₄×C₁₉	—	2	1	no	—
185	C₂×D₄×C₁₉	—	4	1	no	—
186	C₂×D₄×C₁₉	—	4	1	no	—
187	C₂×D₄×C₁₉	—	4	2	no	—
188	C₂×D₄×C₁₉	—	4	2	no	—
189	C₂×D₄×C₁₉	—	4	2	no	—
190	C₂×D₄×C₁₉	—	4	1	no	—
191	C₂×D₄×C₁₉	—	4	2	no	—
192	C₂×D₄×C₁₉	—	4	4	no	—
193	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
194	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
195	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
196	C₂²×C₄×C₁₉	—	2	2	no	—
197	C₂²×C₄×C₁₉	—	2	2	no	—
198	C₂²×C₄×C₁₉	—	2	2	no	—
199	C₂²×C₄×C₁₉	—	2	2	no	—
200	C₂²×C₄×C₁₉	—	2	1	no	—
201	C₂²×C₄×C₁₉	—	2	1	no	—
202	C₂²×C₄×C₁₉	—	2	1	no	—
203	C₂²×C₄×C₁₉	—	4	1	no	—
204	C₂²×C₄×C₁₉	—	4	1	no	—
205	C₂²×C₄×C₁₉	—	4	1	no	—
206	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
210	Q₁₆×C₁₉	—	4	4	no	—
211	SD₁₆×C₁₉	—	4	4	no	—
212	M₁₆×C₁₉	—	2	2	no	—
213	M₁₆×C₁₉	—	4	1	no	—
214	C₂×C₈×C₁₉	—	4	1	no	—
215	C₄⋊C₄×C₁₉	—	2	2	no	—
216	C₄⋊C₄×C₁₉	—	2	2	no	—
217	C₄⋊C₄×C₁₉	—	2	2	no	—
218	C₄⋊C₄×C₁₉	—	2	1	no	—
219	C₄⋊C₄×C₁₉	—	2	1	no	—
220	C₄⋊C₄×C₁₉	—	2	2	no	—
221	C₄⋊C₄×C₁₉	—	2	2	no	—
222	C₄⋊C₄×C₁₉	—	2	1	no	—
223	C₄⋊C₄×C₁₉	—	2	1	no	—
224	C₄⋊C₄×C₁₉	—	2	1	no	—
225	C₄⋊C₄×C₁₉	—	4	1	no	—
226	C₄⋊C₄×C₁₉	—	4	1	no	—
227	C₄⋊C₄×C₁₉	—	4	2	no	—
228	C₂²⋊C₄×C₁₉	—	2	2	no	—
229	C₂²⋊C₄×C₁₉	—	2	2	no	—
230	C₂²⋊C₄×C₁₉	—	2	2	no	—
231	C₂²⋊C₄×C₁₉	—	2	2	no	—
232	C₂²⋊C₄×C₁₉	—	2	2	no	—
233	C₂²⋊C₄×C₁₉	—	2	2	no	—
234	C₂²⋊C₄×C₁₉	—	2	1	no	—
235	C₂²⋊C₄×C₁₉	—	2	1	no	—
236	C₂²⋊C₄×C₁₉	—	2	1	no	—
237	C₂²⋊C₄×C₁₉	—	2	2	no	—
238	C₂²⋊C₄×C₁₉	—	2	2	no	—
239	C₂²⋊C₄×C₁₉	—	2	1	no	—
240	C₂²⋊C₄×C₁₉	—	2	2	no	—
241	C₂²⋊C₄×C₁₉	—	2	2	no	—
242	C₂²⋊C₄×C₁₉	—	2	1	no	—
243	C₂²⋊C₄×C₁₉	—	2	2	no	—
244	C₂²⋊C₄×C₁₉	—	2	2	no	—
245	C₂²⋊C₄×C₁₉	—	4	2	no	—
246	C₂²⋊C₄×C₁₉	—	4	4	no	—
247	C₂²⋊C₄×C₁₉	—	4	2	no	—
248	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
249	C₂²⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
250	C₂²⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
251	C₄²×C₁₉	—	2	2	no	—
252	C₄²×C₁₉	—	2	2	no	—
253	C₄²×C₁₉	—	2	1	no	—
254	C₄²×C₁₉	—	2	1	no	—
255	C₄²×C₁₉	—	4	1	no	—
256	C₄²×C₁₉	—	4	1	no	—
257	C₄²×C₁₉	C₂×D₄	1	2	yes	—
258	#33555	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
259	C₂³×C₁₉	—	2	2	no	—
260	C₂³×C₁₉	—	2	2	no	—
261	C₂³×C₁₉	—	2	2	no	—
262	C₂³×C₁₉	—	2	1	no	—
263	C₂³×C₁₉	—	4	1	no	—
264	C₂³×C₁₉	—	4	1	no	—
265	C₂³×C₁₉	—	4	2	no	—
266	C₂³×C₁₉	—	8	1	no	—
267	C₂³×C₁₉	—	8	2	no	—
268	C₂³×C₁₉	#120	1	1	yes	characteristic
269	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
270	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
271	Q₈×C₁₉	—	2	2	no	—
272	Q₈×C₁₉	—	4	1	no	—
273	Q₈×C₁₉	—	4	2	no	—
274	Q₈×C₁₉	—	4	1	no	—
275	Q₈×C₁₉	—	4	1	no	—
276	Q₈×C₁₉	—	4	1	no	—
277	Q₈×C₁₉	—	4	1	no	—
278	Q₈×C₁₉	—	4	1	no	—
279	Q₈×C₁₉	—	8	2	no	—
280	D₄×C₁₉	—	2	2	no	—
281	D₄×C₁₉	—	4	1	no	—
282	D₄×C₁₉	—	4	1	no	—
283	D₄×C₁₉	—	4	1	no	—
284	D₄×C₁₉	—	4	1	no	—
285	D₄×C₁₉	—	4	1	no	—
286	D₄×C₁₉	—	4	2	no	—
287	D₄×C₁₉	—	4	2	no	—
288	D₄×C₁₉	—	4	2	no	—
289	D₄×C₁₉	—	4	2	no	—
290	D₄×C₁₉	—	4	1	no	—
291	D₄×C₁₉	—	4	1	no	—
292	D₄×C₁₉	—	4	1	no	—
293	D₄×C₁₉	—	8	1	no	—
294	D₄×C₁₉	—	8	1	no	—
295	D₄×C₁₉	—	8	2	no	—
296	D₄×C₁₉	—	8	2	no	—
297	D₄×C₁₉	—	8	2	no	—
298	D₄×C₁₉	—	8	1	no	—
299	D₄×C₁₉	—	8	2	no	—
300	D₄×C₁₉	—	8	4	no	—
301	D₄×C₁₉	—	16	4	no	—
302	C₂×C₄×C₁₉	—	2	1	no	—
303	C₂×C₄×C₁₉	—	2	1	no	—
304	C₂×C₄×C₁₉	—	2	1	no	—
305	C₂×C₄×C₁₉	—	2	1	no	—
306	C₂×C₄×C₁₉	—	2	1	no	—
307	C₂×C₄×C₁₉	—	2	1	no	—
308	C₂×C₄×C₁₉	—	2	2	no	—
309	C₂×C₄×C₁₉	—	2	2	no	—
310	C₂×C₄×C₁₉	—	2	1	no	—
311	C₂×C₄×C₁₉	—	2	2	no	—
312	C₂×C₄×C₁₉	—	2	1	no	—
313	C₂×C₄×C₁₉	—	2	2	no	—
314	C₂×C₄×C₁₉	—	2	2	no	—
315	C₂×C₄×C₁₉	—	2	1	no	—
316	C₂×C₄×C₁₉	—	4	2	no	—
317	C₂×C₄×C₁₉	—	4	2	no	—
318	C₂×C₄×C₁₉	—	4	2	no	—
319	C₂×C₄×C₁₉	—	4	1	no	—
320	C₂×C₄×C₁₉	—	4	2	no	—
321	C₂×C₄×C₁₉	—	4	1	no	—
322	C₂×C₄×C₁₉	—	4	1	no	—
323	C₂×C₄×C₁₉	—	4	1	no	—
324	C₂×C₄×C₁₉	—	4	2	no	—
325	C₂×C₄×C₁₉	—	4	2	no	—
326	C₂×C₄×C₁₉	—	8	1	no	—
327	C₂×C₄×C₁₉	—	8	1	no	—
328	C₂×C₄×C₁₉	—	8	2	no	—
329	C₂×C₄×C₁₉	—	8	2	no	—
330	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
331	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
332	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
333	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
334	C₈×C₁₉	—	4	2	no	—
335	#3540	C₂×C₁₉	1	1	yes	characteristic, complemented
336	#3027	C₂×C₁₉	1	1	yes	characteristic, complemented
337	#3025	C₂×C₁₉	1	1	yes	characteristic, complemented
338	#3022	C₂×C₁₉	1	1	yes	characteristic, complemented
339	#2199	C₂×C₁₉	1	4	yes	complemented
340	#2197	C₂×C₁₉	1	4	yes	complemented
341	#2129	C₂×C₁₉	1	1	yes	characteristic, complemented
342	#2122	C₂×C₁₉	1	1	yes	characteristic, complemented
343	#2120	C₂×C₁₉	1	1	yes	characteristic, complemented
344	C₂²×C₁₉	—	2	1	no	—
345	C₂²×C₁₉	—	2	1	no	—
346	C₂²×C₁₉	—	2	1	no	—
347	C₂²×C₁₉	—	4	1	no	—
348	C₂²×C₁₉	—	4	1	no	—
349	C₂²×C₁₉	—	4	1	no	—
350	C₂²×C₁₉	—	4	2	no	—
351	C₂²×C₁₉	—	4	1	no	—
352	C₂²×C₁₉	—	4	1	no	—
353	C₂²×C₁₉	—	4	2	no	—
354	C₂²×C₁₉	—	4	2	no	—
355	C₂²×C₁₉	—	4	2	no	—
356	C₂²×C₁₉	—	4	1	no	—
357	C₂²×C₁₉	—	4	2	no	—
358	C₂²×C₁₉	—	8	2	no	—
359	C₂²×C₁₉	—	8	2	no	—
360	C₂²×C₁₉	—	8	4	no	—
361	C₂²×C₁₉	—	8	1	no	—
362	C₂²×C₁₉	—	16	1	no	—
363	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
364	C₄×C₁₉	—	2	1	no	—
365	C₄×C₁₉	—	2	1	no	—
366	C₄×C₁₉	—	2	1	no	—
367	C₄×C₁₉	—	4	1	no	—
368	C₄×C₁₉	—	4	2	no	—
369	C₄×C₁₉	—	4	2	no	—
370	C₄×C₁₉	—	4	1	no	—
371	C₄×C₁₉	—	4	2	no	—
372	C₄×C₁₉	—	4	1	no	—
373	C₄×C₁₉	—	4	2	no	—
374	C₄×C₁₉	—	8	2	no	—
375	C₄×C₁₉	—	8	2	no	—
376	C₄×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
377	C₄×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
378	#585	C₂²×C₁₉	1	1	yes	characteristic
379	C₂×#137	—	2	1	no	—
380	H(3,𝔽₄)	C₂²×C₁₉	1	2	yes	complemented
381	#560	—	2	1	no	—
382	#559	—	2	1	no	—
383	#556	—	2	1	no	—
384	#555	—	2	1	no	—
385	#551	C₂²×C₁₉	1	2	yes	complemented
386	#548	—	2	1	no	—
387	#546	—	2	1	no	—
388	#542	—	2	2	no	—
389	#542	—	2	1	no	—
390	#538	—	2	2	no	—
391	#536	C₂²×C₁₉	1	1	yes	characteristic
392	#535	—	2	1	no	—
393	#535	C₂²×C₁₉	1	1	yes	characteristic
394	#525	—	2	1	no	—
395	#525	—	2	1	no	—
396	#525	C₂²×C₁₉	1	1	yes	characteristic
397	#458	—	2	1	no	—
398	#458	C₂²×C₁₉	1	2	yes	—
399	B(4,𝔽₂)	—	2	1	no	—
400	B(4,𝔽₂)	—	2	2	no	—
401	B(4,𝔽₂)	C₂²×C₁₉	1	4	yes	—
402	B(4,𝔽₂)	C₂²×C₁₉	1	2	yes	—
403	#456	—	2	2	no	—
404	#455	C₂²×C₁₉	1	4	yes	—
405	#421	—	2	1	no	—
406	#413	C₂²×C₁₉	1	1	yes	characteristic
407	#410	—	2	1	no	—
408	#410	—	2	1	no	—
409	#410	C₂²×C₁₉	1	1	yes	characteristic
410	#410	C₂²×C₁₉	1	1	yes	characteristic
411	#354	C₂²×C₁₉	1	4	yes	complemented
412	#352	C₂²×C₁₉	1	2	yes	complemented
413	AΣL(1,𝔽₁₆)	C₂²×C₁₉	1	2	yes	complemented
414	AΣL(1,𝔽₁₆)	C₂²×C₁₉	1	4	yes	complemented
415	C₂×C₁₉	—	2	1	no	—
416	C₂×C₁₉	—	4	1	no	—
417	C₂×C₁₉	—	4	1	no	—
418	C₂×C₁₉	—	4	1	no	—
419	C₂×C₁₉	—	8	1	no	—
420	C₂×C₁₉	—	8	2	no	—
421	C₂×C₁₉	—	8	2	no	—
422	C₂×C₁₉	C₂×B(4,𝔽₂)	1	1	yes	characteristic
423	2₋¹⁺⁴	—	2	1	no	—
424	2₋¹⁺⁴	—	4	1	no	—
425	H(5,𝔽₂)	—	2	1	no	—
426	H(5,𝔽₂)	—	2	1	no	—
427	H(5,𝔽₂)	—	4	1	no	—
428	H(5,𝔽₂)	C₂³×C₁₉	1	2	yes	—
429	C₂×#41	—	2	1	no	—
430	C₂×#41	—	2	1	no	—
431	C₂×#41	—	2	1	no	—
432	C₂×#41	—	2	1	no	—
433	C₂×#41	—	4	2	no	—
434	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
435	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic, complemented
436	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic, complemented
437	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic, complemented
438	#137	—	2	4	no	—
439	#137	—	4	2	no	—
440	C₂×Q₁₆	—	4	1	no	—
441	C₂×SD₁₆	—	4	1	no	—
442	C₂×M₁₆	—	2	1	no	—
443	C₄⋊Q₈	—	2	1	no	—
444	C₄⋊Q₈	D₄×C₁₉	1	2	yes	complemented
445	#127	—	2	1	no	—
446	#127	—	4	1	no	—
447	#126	—	2	2	no	—
448	#126	—	2	2	no	—
449	#126	—	2	2	no	—
450	#124	—	2	2	no	—
451	#124	—	2	1	no	—
452	#124	—	2	1	no	—
453	#124	—	2	2	no	—
454	#124	—	2	2	no	—
455	#124	—	2	2	no	—
456	#124	—	2	2	no	—
457	#124	—	4	1	no	—
458	#124	C₂³×C₁₉	1	2	yes	—
459	#123	—	2	2	no	—
460	#123	—	2	2	no	—
461	#123	—	2	1	no	—
462	#123	—	2	1	no	—
463	#123	—	2	2	no	—
464	#123	—	2	2	no	—
465	#123	D₄×C₁₉	1	1	yes	characteristic, complemented
466	#123	C₂³×C₁₉	1	1	yes	characteristic
467	C₂²⋊Q₈	—	2	1	no	—
468	C₂²⋊Q₈	—	2	2	no	—
469	C₂²⋊Q₈	—	2	1	no	—
470	C₂²⋊Q₈	—	2	2	no	—
471	C₂²⋊Q₈	—	2	1	no	—
472	C₂²⋊Q₈	—	2	1	no	—
473	C₂²⋊Q₈	—	4	1	no	—
474	#121	—	2	1	no	—
475	#121	—	2	2	no	—
476	#121	—	2	2	no	—
477	#121	—	2	2	no	—
478	#121	—	2	1	no	—
479	#121	—	2	1	no	—
480	#121	—	2	1	no	—
481	#121	—	4	2	no	—
482	#121	—	4	1	no	—
483	#120	—	2	2	no	—
484	#120	—	2	2	no	—
485	#120	—	2	2	no	—
486	#120	—	2	4	no	—
487	#120	D₄×C₁₉	1	1	yes	characteristic, complemented
488	#120	D₄×C₁₉	1	2	yes	complemented
489	#120	C₂³×C₁₉	1	1	yes	characteristic
490	#120	C₂³×C₁₉	1	2	yes	—
491	C₄×Q₈	—	2	1	no	—
492	C₄×Q₈	—	2	2	no	—
493	C₄×D₄	—	2	2	no	—
494	C₄×D₄	—	2	2	no	—
495	C₄×D₄	—	2	1	no	—
496	C₄×D₄	—	2	2	no	—
497	C₄×D₄	—	2	1	no	—
498	C₄×D₄	—	2	1	no	—
499	C₄×D₄	—	4	2	no	—
500	#117	—	2	1	no	—
501	#117	—	2	2	no	—
502	#117	—	2	1	no	—
503	#117	—	2	1	no	—
504	#117	D₄×C₁₉	1	1	yes	characteristic, complemented
505	#117	D₄×C₁₉	1	1	yes	characteristic, complemented
506	#117	D₄×C₁₉	1	1	yes	characteristic, complemented
507	C₂×C₂²⋊C₄	—	2	2	no	—
508	#104	—	2	4	no	—
509	#101	—	2	1	no	—
510	#100	C₂³×C₁₉	1	2	yes	—
511	#99	—	2	1	no	—
512	#99	—	2	1	no	—
513	#99	—	2	4	no	—
514	#99	—	2	2	no	—
515	#99	—	2	2	no	—
516	#99	C₂³×C₁₉	1	2	yes	—
517	#99	C₂³×C₁₉	1	2	yes	—
518	C₁₉	#33555	1	1	yes	characteristic, direct product factor, Sylow
519	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
520	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
521	#41	—	2	2	no	—
522	#41	—	2	2	no	—
523	#41	—	4	1	no	—
524	#41	—	4	1	no	—
525	#41	—	4	2	no	—
526	#41	—	4	1	no	—
527	#41	—	4	1	no	—
528	#41	—	4	1	no	—
529	#41	—	4	1	no	—
530	#41	—	4	1	no	—
531	#41	—	4	2	no	—
532	#41	—	4	2	no	—
533	#41	—	4	2	no	—
534	#41	—	4	1	no	—
535	#41	—	4	1	no	—
536	#41	—	4	1	no	—
537	#41	—	8	1	no	—
538	#41	—	8	1	no	—
539	C₂×Q₈	—	2	1	no	—
540	C₂×Q₈	—	2	1	no	—
541	C₂×Q₈	—	2	2	no	—
542	C₂×Q₈	—	2	1	no	—
543	C₂×Q₈	—	2	1	no	—
544	C₂×Q₈	—	4	1	no	—
545	C₂×Q₈	—	4	1	no	—
546	C₂×Q₈	—	4	2	no	—
547	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
548	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
549	C₂×D₄	—	2	1	no	—
550	C₂×D₄	—	2	1	no	—
551	C₂×D₄	—	2	1	no	—
552	C₂×D₄	—	2	2	no	—
553	C₂×D₄	—	2	2	no	—
554	C₂×D₄	—	2	2	no	—
555	C₂×D₄	—	2	2	no	—
556	C₂×D₄	—	2	1	no	—
557	C₂×D₄	—	2	2	no	—
558	C₂×D₄	—	2	1	no	—
559	C₂×D₄	—	2	2	no	—
560	C₂×D₄	—	2	1	no	—
561	C₂×D₄	—	2	1	no	—
562	C₂×D₄	—	4	1	no	—
563	C₂×D₄	—	4	1	no	—
564	C₂×D₄	—	4	2	no	—
565	C₂×D₄	—	4	2	no	—
566	C₂×D₄	—	4	2	no	—
567	C₂×D₄	—	4	1	no	—
568	C₂×D₄	—	4	2	no	—
569	C₂×D₄	—	4	4	no	—
570	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
571	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
572	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
573	C₂²×C₄	—	2	2	no	—
574	C₂²×C₄	—	2	2	no	—
575	C₂²×C₄	—	2	2	no	—
576	C₂²×C₄	—	2	2	no	—
577	C₂²×C₄	—	2	1	no	—
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	2	1	no	—
580	C₂²×C₄	—	4	1	no	—
581	C₂²×C₄	—	4	1	no	—
582	C₂²×C₄	—	4	1	no	—
583	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
584	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
585	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
586	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
587	Q₁₆	—	4	4	no	—
588	SD₁₆	—	4	4	no	—
589	M₁₆	—	2	2	no	—
590	M₁₆	—	4	1	no	—
591	C₂×C₈	—	4	1	no	—
592	C₄⋊C₄	—	2	2	no	—
593	C₄⋊C₄	—	2	2	no	—
594	C₄⋊C₄	—	2	2	no	—
595	C₄⋊C₄	—	2	1	no	—
596	C₄⋊C₄	—	2	1	no	—
597	C₄⋊C₄	—	2	1	no	—
598	C₄⋊C₄	—	2	1	no	—
599	C₄⋊C₄	—	2	2	no	—
600	C₄⋊C₄	—	2	2	no	—
601	C₄⋊C₄	—	2	1	no	—
602	C₄⋊C₄	—	4	1	no	—
603	C₄⋊C₄	—	4	1	no	—
604	C₄⋊C₄	—	4	2	no	—
605	C₂²⋊C₄	—	2	2	no	—
606	C₂²⋊C₄	—	2	2	no	—
607	C₂²⋊C₄	—	2	2	no	—
608	C₂²⋊C₄	—	2	2	no	—
609	C₂²⋊C₄	—	2	2	no	—
610	C₂²⋊C₄	—	2	2	no	—
611	C₂²⋊C₄	—	2	1	no	—
612	C₂²⋊C₄	—	2	1	no	—
613	C₂²⋊C₄	—	2	1	no	—
614	C₂²⋊C₄	—	2	2	no	—
615	C₂²⋊C₄	—	2	2	no	—
616	C₂²⋊C₄	—	2	1	no	—
617	C₂²⋊C₄	—	2	2	no	—
618	C₂²⋊C₄	—	2	2	no	—
619	C₂²⋊C₄	—	2	1	no	—
620	C₂²⋊C₄	—	2	2	no	—
621	C₂²⋊C₄	—	2	2	no	—
622	C₂²⋊C₄	—	4	2	no	—
623	C₂²⋊C₄	—	4	4	no	—
624	C₂²⋊C₄	—	4	2	no	—
625	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
626	C₂²⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
627	C₂²⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
628	C₄²	—	2	2	no	—
629	C₄²	—	2	2	no	—
630	C₄²	—	2	1	no	—
631	C₄²	—	2	1	no	—
632	C₄²	—	4	1	no	—
633	C₄²	—	4	1	no	—
634	C₄²	C₂×D₄×C₁₉	1	2	yes	—
635	C₂³	—	2	2	no	—
636	C₂³	—	2	2	no	—
637	C₂³	—	2	2	no	—
638	C₂³	—	2	1	no	—
639	C₂³	—	4	1	no	—
640	C₂³	—	4	1	no	—
641	C₂³	—	4	2	no	—
642	C₂³	—	8	1	no	—
643	C₂³	—	8	2	no	—
644	C₂³	C₁₉×#120	1	1	yes	characteristic
645	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
646	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
647	Q₈	—	2	2	no	—
648	Q₈	—	4	1	no	—
649	Q₈	—	4	2	no	—
650	Q₈	—	4	1	no	—
651	Q₈	—	4	1	no	—
652	Q₈	—	4	1	no	—
653	Q₈	—	4	1	no	—
654	Q₈	—	4	1	no	—
655	Q₈	—	8	2	no	—
656	D₄	—	2	2	no	—
657	D₄	—	4	1	no	—
658	D₄	—	4	1	no	—
659	D₄	—	4	1	no	—
660	D₄	—	4	1	no	—
661	D₄	—	4	1	no	—
662	D₄	—	4	2	no	—
663	D₄	—	4	2	no	—
664	D₄	—	4	2	no	—
665	D₄	—	4	2	no	—
666	D₄	—	4	1	no	—
667	D₄	—	4	1	no	—
668	D₄	—	4	1	no	—
669	D₄	—	8	1	no	—
670	D₄	—	8	2	no	—
671	D₄	—	8	1	no	—
672	D₄	—	8	2	no	—
673	D₄	—	8	2	no	—
674	D₄	—	8	2	no	—
675	D₄	—	8	1	no	—
676	D₄	—	8	4	no	—
677	D₄	—	16	4	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	4	2	no	—
693	C₂×C₄	—	4	2	no	—
694	C₂×C₄	—	4	2	no	—
695	C₂×C₄	—	4	1	no	—
696	C₂×C₄	—	4	2	no	—
697	C₂×C₄	—	4	1	no	—
698	C₂×C₄	—	4	1	no	—
699	C₂×C₄	—	4	1	no	—
700	C₂×C₄	—	4	2	no	—
701	C₂×C₄	—	4	2	no	—
702	C₂×C₄	—	8	1	no	—
703	C₂×C₄	—	8	1	no	—
704	C₂×C₄	—	8	2	no	—
705	C₂×C₄	—	8	2	no	—
706	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
707	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
708	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
709	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
710	C₈	—	4	2	no	—
711	C₂²	—	2	1	no	—
712	C₂²	—	2	1	no	—
713	C₂²	—	2	1	no	—
714	C₂²	—	4	1	no	—
715	C₂²	—	4	1	no	—
716	C₂²	—	4	1	no	—
717	C₂²	—	4	2	no	—
718	C₂²	—	4	1	no	—
719	C₂²	—	4	1	no	—
720	C₂²	—	4	2	no	—
721	C₂²	—	4	2	no	—
722	C₂²	—	4	2	no	—
723	C₂²	—	4	1	no	—
724	C₂²	—	4	2	no	—
725	C₂²	—	8	2	no	—
726	C₂²	—	8	2	no	—
727	C₂²	—	8	4	no	—
728	C₂²	—	8	1	no	—
729	C₂²	—	16	1	no	—
730	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
731	C₄	—	2	1	no	—
732	C₄	—	2	1	no	—
733	C₄	—	2	1	no	—
734	C₄	—	4	1	no	—
735	C₄	—	4	2	no	—
736	C₄	—	4	2	no	—
737	C₄	—	4	1	no	—
738	C₄	—	4	2	no	—
739	C₄	—	4	1	no	—
740	C₄	—	4	2	no	—
741	C₄	—	8	2	no	—
742	C₄	—	8	2	no	—
743	C₄	C₁₉×B(4,𝔽₂)	1	1	yes	characteristic
744	C₄	C₁₉×B(4,𝔽₂)	1	1	yes	characteristic
745	C₂	—	2	1	no	—
746	C₂	—	4	1	no	—
747	C₂	—	4	1	no	—
748	C₂	—	4	1	no	—
749	C₂	—	8	1	no	—
750	C₂	—	8	2	no	—
751	C₂	—	8	2	no	—
752	C₂	C₂×C₁₉×B(4,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₉	C₂×B(4,𝔽₂)
commutator, Frattini, cosocle	C₂×D₄	C₂⁴×C₁₉
LCS	G ▷ C₂×D₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂×#41×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3540	C₂	semidirect
2. C₁₉×#3027	C₂	semidirect
3. C₁₉×#3025	C₂	semidirect
4. C₁₉×#3022	C₂	semidirect
5. C₁₉×#2199	C₂	semidirect
6. C₁₉×#2197	C₂	semidirect
7. C₁₉×#2129	C₂	semidirect
8. C₁₉×#2122	C₂	semidirect
9. C₁₉×#2120	C₂	semidirect
12. C₁₉×H(3,𝔽₄)	C₂²	semidirect
17. C₁₉×#551	C₂²	semidirect
43. C₁₉×#354	C₂²	semidirect
44. C₁₉×#352	C₂²	semidirect
45. C₁₉×AΣL(1,𝔽₁₆)	C₂²	semidirect
46. C₁₉×AΣL(1,𝔽₁₆)	C₂²	semidirect
59. C₂²×Q₈×C₁₉	D₄	semidirect
60. C₂²×D₄×C₁₉	D₄	semidirect
61. C₂³×C₄×C₁₉	D₄	semidirect
68. C₁₉×C₄⋊Q₈	D₄	semidirect
89. C₁₉×#123	D₄	semidirect
111. C₁₉×#120	D₄	semidirect
112. C₁₉×#120	D₄	semidirect
128. C₁₉×#117	D₄	semidirect
129. C₁₉×#117	D₄	semidirect
130. C₁₉×#117	D₄	semidirect
258. #33555	C₁₉	direct (N × H)
335. #3540	C₂×C₁₉	semidirect
336. #3027	C₂×C₁₉	semidirect
337. #3025	C₂×C₁₉	semidirect
338. #3022	C₂×C₁₉	semidirect
339. #2199	C₂×C₁₉	semidirect
340. #2197	C₂×C₁₉	semidirect
341. #2129	C₂×C₁₉	semidirect
342. #2122	C₂×C₁₉	semidirect
343. #2120	C₂×C₁₉	semidirect
380. H(3,𝔽₄)	C₂²×C₁₉	semidirect
385. #551	C₂²×C₁₉	semidirect
411. #354	C₂²×C₁₉	semidirect
412. #352	C₂²×C₁₉	semidirect
413. AΣL(1,𝔽₁₆)	C₂²×C₁₉	semidirect
414. AΣL(1,𝔽₁₆)	C₂²×C₁₉	semidirect
435. C₂²×Q₈	D₄×C₁₉	semidirect
436. C₂²×D₄	D₄×C₁₉	semidirect
437. C₂³×C₄	D₄×C₁₉	semidirect
444. C₄⋊Q₈	D₄×C₁₉	semidirect
465. #123	D₄×C₁₉	semidirect
487. #120	D₄×C₁₉	semidirect
488. #120	D₄×C₁₉	semidirect
504. #117	D₄×C₁₉	semidirect
505. #117	D₄×C₁₉	semidirect
506. #117	D₄×C₁₉	semidirect
518. C₁₉	#33555	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×#3540	2
C₁₉×#3027	2
C₁₉×#3025	2
C₁₉×#3022	2
C₁₉×#2199	2
C₁₉×#2197	2
C₁₉×#2129	2
C₁₉×#2122	2
C₁₉×#2120	2
#33555	19

Subgroups — C19×#33555 #18039514

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#33555 #18039514