Subgroups — C₁₉×#33553 #18039512

Order 4864.

1252 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3537	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×#3021	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2200	C₂	1	4	yes	maximal, complemented
6	C₁₉×#2196	C₂	1	4	yes	maximal, complemented
7	C₁₉×#2128	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, complemented
11	C₂×C₁₉×AGL(1,ℤ/8)	—	2	1	no	—
12	C₁₉×#560	—	2	1	no	—
13	C₁₉×#560	C₂²	1	2	yes	complemented
14	C₁₉×#553	—	2	1	no	—
15	C₁₉×#553	—	2	1	no	—
16	D₄²×C₁₉	—	2	1	no	—
17	D₄²×C₁₉	—	2	1	no	—
18	D₄²×C₁₉	—	2	1	no	—
19	D₄²×C₁₉	C₂²	1	2	yes	complemented
20	C₁₉×#540	—	2	1	no	—
21	C₁₉×#538	—	2	2	no	—
22	C₁₉×#535	—	2	1	no	—
23	C₁₉×#535	C₂²	1	1	yes	characteristic
24	C₁₉×#535	C₂²	1	1	yes	characteristic
25	C₁₉×#534	—	2	2	no	—
26	C₁₉×#525	—	2	1	no	—
27	C₁₉×#525	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#121	—	2	1	no	—
29	C₁₉×#458	—	2	1	no	—
30	C₁₉×#458	C₂²	1	2	yes	complemented
31	C₁₉×B(4,𝔽₂)	—	2	1	no	—
32	C₁₉×B(4,𝔽₂)	—	2	2	no	—
33	C₁₉×B(4,𝔽₂)	C₂²	1	2	yes	complemented
34	C₁₉×B(4,𝔽₂)	C₂²	1	4	yes	complemented
35	C₁₉×#454	—	2	2	no	—
36	C₁₉×#453	C₂²	1	4	yes	complemented
37	C₁₉×#421	—	2	1	no	—
38	C₁₉×#413	C₂²	1	1	yes	characteristic, complemented
39	C₁₉×#410	—	2	1	no	—
40	C₁₉×#410	—	2	1	no	—
41	C₁₉×#410	C₂²	1	1	yes	characteristic, complemented
42	C₁₉×#410	C₂²	1	1	yes	characteristic, complemented
43	C₁₉×#353	C₂²	1	4	yes	complemented
44	C₁₉×#352	C₂²	1	2	yes	complemented
45	C₁₉×AΣL(1,𝔽₁₆)	C₂²	1	2	yes	complemented
46	C₁₉×AΣL(1,𝔽₁₆)	C₂²	1	4	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	—	4	2	no	—
57	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
58	C₂²×D₄×C₁₉	—	2	1	no	—
59	C₂²×D₄×C₁₉	—	2	2	no	—
60	C₂²×D₄×C₁₉	—	2	2	no	—
61	C₂²×D₄×C₁₉	—	2	2	no	—
62	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic, complemented
63	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic, complemented
64	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic, complemented
65	C₁₉×AGL(1,ℤ/8)	—	2	4	no	—
66	C₁₉×AGL(1,ℤ/8)	—	4	2	no	—
67	C₂×SD₁₆×C₁₉	—	4	1	no	—
68	C₂×D₈×C₁₉	—	4	1	no	—
69	C₂×M₁₆×C₁₉	—	2	1	no	—
70	C₁₉×#127	—	2	1	no	—
71	C₁₉×#127	—	2	1	no	—
72	C₁₉×#127	—	4	1	no	—
73	C₁₉×#127	C₂³	1	2	yes	—
74	C₁₉×#126	—	2	2	no	—
75	C₁₉×#126	—	2	2	no	—
76	C₁₉×#125	—	2	1	no	—
77	C₁₉×#124	—	2	1	no	—
78	C₁₉×#124	—	4	1	no	—
79	C₁₉×#124	D₄	1	2	yes	complemented
80	C₁₉×#123	—	2	2	no	—
81	C₁₉×#123	—	2	2	no	—
82	C₁₉×#123	—	2	2	no	—
83	C₁₉×#123	—	2	2	no	—
84	C₁₉×#123	—	2	2	no	—
85	C₁₉×#123	D₄	1	1	yes	characteristic, complemented
86	C₁₉×#123	C₂³	1	1	yes	characteristic
87	C₁₉×C₂²⋊Q₈	—	2	1	no	—
88	C₁₉×C₂²⋊Q₈	—	4	1	no	—
89	C₁₉×#121	—	2	2	no	—
90	C₁₉×#121	—	2	1	no	—
91	C₁₉×#121	—	2	1	no	—
92	C₁₉×#121	—	2	2	no	—
93	C₁₉×#121	—	2	2	no	—
94	C₁₉×#121	—	2	1	no	—
95	C₁₉×#121	—	2	2	no	—
96	C₁₉×#121	—	2	1	no	—
97	C₁₉×#121	—	2	1	no	—
98	C₁₉×#121	—	2	2	no	—
99	C₁₉×#121	—	2	1	no	—
100	C₁₉×#121	—	2	1	no	—
101	C₁₉×#121	—	2	2	no	—
102	C₁₉×#121	—	2	2	no	—
103	C₁₉×#121	—	2	2	no	—
104	C₁₉×#121	—	4	2	no	—
105	C₁₉×#121	—	4	1	no	—
106	C₁₉×#120	—	2	2	no	—
107	C₁₉×#120	—	2	2	no	—
108	C₁₉×#120	—	2	2	no	—
109	C₁₉×#120	—	2	1	no	—
110	C₁₉×#120	—	2	1	no	—
111	C₁₉×#120	—	2	2	no	—
112	C₁₉×#120	—	2	2	no	—
113	C₁₉×#120	—	2	4	no	—
114	C₁₉×#120	D₄	1	1	yes	characteristic, complemented
115	C₁₉×#120	D₄	1	2	yes	complemented
116	C₁₉×#120	C₂³	1	1	yes	characteristic
117	C₁₉×#120	C₂³	1	2	yes	—
118	C₄×D₄×C₁₉	—	2	2	no	—
119	C₄×D₄×C₁₉	—	2	1	no	—
120	C₄×D₄×C₁₉	—	2	1	no	—
121	C₄×D₄×C₁₉	—	2	1	no	—
122	C₄×D₄×C₁₉	—	2	1	no	—
123	C₄×D₄×C₁₉	—	2	2	no	—
124	C₄×D₄×C₁₉	—	4	2	no	—
125	C₁₉×#117	—	2	1	no	—
126	C₁₉×#117	—	2	1	no	—
127	C₁₉×#117	D₄	1	1	yes	characteristic, complemented
128	C₁₉×#117	D₄	1	1	yes	characteristic, complemented
129	C₁₉×#117	D₄	1	1	yes	characteristic, complemented
130	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
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	—	2	2	no	—
143	C₂⁴×C₁₉	—	2	1	no	—
144	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
145	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
146	#41×C₁₉	—	2	2	no	—
147	#41×C₁₉	—	2	2	no	—
148	#41×C₁₉	—	4	1	no	—
149	#41×C₁₉	—	4	1	no	—
150	#41×C₁₉	—	4	2	no	—
151	#41×C₁₉	—	4	1	no	—
152	#41×C₁₉	—	4	1	no	—
153	#41×C₁₉	—	4	1	no	—
154	#41×C₁₉	—	4	1	no	—
155	#41×C₁₉	—	4	1	no	—
156	#41×C₁₉	—	4	2	no	—
157	#41×C₁₉	—	4	2	no	—
158	#41×C₁₉	—	4	2	no	—
159	#41×C₁₉	—	4	1	no	—
160	#41×C₁₉	—	4	1	no	—
161	#41×C₁₉	—	4	1	no	—
162	C₂×Q₈×C₁₉	—	2	1	no	—
163	C₂×Q₈×C₁₉	—	2	1	no	—
164	C₂×Q₈×C₁₉	—	2	1	no	—
165	C₂×Q₈×C₁₉	—	4	2	no	—
166	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
167	C₂×D₄×C₁₉	—	2	1	no	—
168	C₂×D₄×C₁₉	—	2	2	no	—
169	C₂×D₄×C₁₉	—	2	2	no	—
170	C₂×D₄×C₁₉	—	2	1	no	—
171	C₂×D₄×C₁₉	—	2	1	no	—
172	C₂×D₄×C₁₉	—	2	1	no	—
173	C₂×D₄×C₁₉	—	2	1	no	—
174	C₂×D₄×C₁₉	—	2	2	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	2	no	—
180	C₂×D₄×C₁₉	—	2	2	no	—
181	C₂×D₄×C₁₉	—	2	2	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	—	2	1	no	—
186	C₂×D₄×C₁₉	—	4	1	no	—
187	C₂×D₄×C₁₉	—	4	1	no	—
188	C₂×D₄×C₁₉	—	4	1	no	—
189	C₂×D₄×C₁₉	—	4	1	no	—
190	C₂×D₄×C₁₉	—	4	2	no	—
191	C₂×D₄×C₁₉	—	4	2	no	—
192	C₂×D₄×C₁₉	—	4	2	no	—
193	C₂×D₄×C₁₉	—	4	1	no	—
194	C₂×D₄×C₁₉	—	4	2	no	—
195	C₂×D₄×C₁₉	—	4	4	no	—
196	C₂×D₄×C₁₉	—	8	1	no	—
197	C₂×D₄×C₁₉	—	8	1	no	—
198	C₂×D₄×C₁₉	—	8	4	no	—
199	C₂×D₄×C₁₉	—	8	4	no	—
200	C₂×D₄×C₁₉	—	8	4	no	—
201	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
202	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
203	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
204	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
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	1	no	—
211	C₂²×C₄×C₁₉	—	2	1	no	—
212	C₂²×C₄×C₁₉	—	4	1	no	—
213	C₂²×C₄×C₁₉	—	4	1	no	—
214	C₂²×C₄×C₁₉	—	4	1	no	—
215	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
219	SD₁₆×C₁₉	—	4	4	no	—
220	D₈×C₁₉	—	4	4	no	—
221	M₁₆×C₁₉	—	2	2	no	—
222	M₁₆×C₁₉	—	4	1	no	—
223	C₂×C₈×C₁₉	—	4	1	no	—
224	C₄⋊C₄×C₁₉	—	2	2	no	—
225	C₄⋊C₄×C₁₉	—	2	2	no	—
226	C₄⋊C₄×C₁₉	—	2	2	no	—
227	C₄⋊C₄×C₁₉	—	2	1	no	—
228	C₄⋊C₄×C₁₉	—	2	1	no	—
229	C₄⋊C₄×C₁₉	—	2	1	no	—
230	C₄⋊C₄×C₁₉	—	2	1	no	—
231	C₄⋊C₄×C₁₉	—	2	1	no	—
232	C₄⋊C₄×C₁₉	—	4	1	no	—
233	C₄⋊C₄×C₁₉	—	4	1	no	—
234	C₄⋊C₄×C₁₉	—	4	2	no	—
235	C₂²⋊C₄×C₁₉	—	2	2	no	—
236	C₂²⋊C₄×C₁₉	—	2	2	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	1	no	—
241	C₂²⋊C₄×C₁₉	—	2	1	no	—
242	C₂²⋊C₄×C₁₉	—	2	2	no	—
243	C₂²⋊C₄×C₁₉	—	2	2	no	—
244	C₂²⋊C₄×C₁₉	—	2	1	no	—
245	C₂²⋊C₄×C₁₉	—	2	2	no	—
246	C₂²⋊C₄×C₁₉	—	2	1	no	—
247	C₂²⋊C₄×C₁₉	—	2	2	no	—
248	C₂²⋊C₄×C₁₉	—	2	2	no	—
249	C₂²⋊C₄×C₁₉	—	2	2	no	—
250	C₂²⋊C₄×C₁₉	—	4	2	no	—
251	C₂²⋊C₄×C₁₉	—	4	4	no	—
252	C₂²⋊C₄×C₁₉	—	4	2	no	—
253	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
254	C₂²⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
255	C₂²⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
256	C₄²×C₁₉	—	2	1	no	—
257	C₄²×C₁₉	—	2	1	no	—
258	C₄²×C₁₉	—	4	1	no	—
259	C₄²×C₁₉	—	4	1	no	—
260	C₄²×C₁₉	C₂×D₄	1	2	yes	—
261	#33553	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
262	C₂³×C₁₉	—	2	1	no	—
263	C₂³×C₁₉	—	2	2	no	—
264	C₂³×C₁₉	—	2	2	no	—
265	C₂³×C₁₉	—	2	2	no	—
266	C₂³×C₁₉	—	2	2	no	—
267	C₂³×C₁₉	—	4	1	no	—
268	C₂³×C₁₉	—	4	2	no	—
269	C₂³×C₁₉	—	4	1	no	—
270	C₂³×C₁₉	—	4	4	no	—
271	C₂³×C₁₉	—	4	2	no	—
272	C₂³×C₁₉	—	8	1	no	—
273	C₂³×C₁₉	—	8	2	no	—
274	C₂³×C₁₉	—	8	2	no	—
275	C₂³×C₁₉	—	8	2	no	—
276	C₂³×C₁₉	—	8	2	no	—
277	C₂³×C₁₉	#120	1	1	yes	characteristic
278	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
279	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
280	Q₈×C₁₉	—	2	2	no	—
281	Q₈×C₁₉	—	4	1	no	—
282	Q₈×C₁₉	—	4	1	no	—
283	Q₈×C₁₉	—	4	1	no	—
284	Q₈×C₁₉	—	4	1	no	—
285	D₄×C₁₉	—	2	2	no	—
286	D₄×C₁₉	—	4	1	no	—
287	D₄×C₁₉	—	4	1	no	—
288	D₄×C₁₉	—	4	1	no	—
289	D₄×C₁₉	—	4	2	no	—
290	D₄×C₁₉	—	4	1	no	—
291	D₄×C₁₉	—	4	1	no	—
292	D₄×C₁₉	—	4	2	no	—
293	D₄×C₁₉	—	4	2	no	—
294	D₄×C₁₉	—	4	2	no	—
295	D₄×C₁₉	—	4	2	no	—
296	D₄×C₁₉	—	4	4	no	—
297	D₄×C₁₉	—	4	4	no	—
298	D₄×C₁₉	—	4	2	no	—
299	D₄×C₁₉	—	4	2	no	—
300	D₄×C₁₉	—	4	1	no	—
301	D₄×C₁₉	—	4	1	no	—
302	D₄×C₁₉	—	4	1	no	—
303	D₄×C₁₉	—	4	1	no	—
304	D₄×C₁₉	—	4	1	no	—
305	D₄×C₁₉	—	8	1	no	—
306	D₄×C₁₉	—	8	2	no	—
307	D₄×C₁₉	—	8	2	no	—
308	D₄×C₁₉	—	8	2	no	—
309	D₄×C₁₉	—	8	2	no	—
310	D₄×C₁₉	—	8	2	no	—
311	D₄×C₁₉	—	8	2	no	—
312	D₄×C₁₉	—	8	2	no	—
313	D₄×C₁₉	—	8	4	no	—
314	D₄×C₁₉	—	16	4	no	—
315	C₂×C₄×C₁₉	—	2	1	no	—
316	C₂×C₄×C₁₉	—	2	1	no	—
317	C₂×C₄×C₁₉	—	2	1	no	—
318	C₂×C₄×C₁₉	—	2	1	no	—
319	C₂×C₄×C₁₉	—	2	1	no	—
320	C₂×C₄×C₁₉	—	2	1	no	—
321	C₂×C₄×C₁₉	—	2	2	no	—
322	C₂×C₄×C₁₉	—	2	2	no	—
323	C₂×C₄×C₁₉	—	2	2	no	—
324	C₂×C₄×C₁₉	—	2	1	no	—
325	C₂×C₄×C₁₉	—	2	1	no	—
326	C₂×C₄×C₁₉	—	2	2	no	—
327	C₂×C₄×C₁₉	—	2	1	no	—
328	C₂×C₄×C₁₉	—	4	2	no	—
329	C₂×C₄×C₁₉	—	4	2	no	—
330	C₂×C₄×C₁₉	—	4	2	no	—
331	C₂×C₄×C₁₉	—	4	1	no	—
332	C₂×C₄×C₁₉	—	4	2	no	—
333	C₂×C₄×C₁₉	—	4	1	no	—
334	C₂×C₄×C₁₉	—	4	1	no	—
335	C₂×C₄×C₁₉	—	4	1	no	—
336	C₂×C₄×C₁₉	—	4	2	no	—
337	C₂×C₄×C₁₉	—	4	2	no	—
338	C₂×C₄×C₁₉	—	8	1	no	—
339	C₂×C₄×C₁₉	—	8	2	no	—
340	C₂×C₄×C₁₉	—	8	2	no	—
341	C₂×C₄×C₁₉	—	8	2	no	—
342	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
343	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
344	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
345	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
346	C₈×C₁₉	—	4	2	no	—
347	#3537	C₂×C₁₉	1	1	yes	characteristic, complemented
348	#3027	C₂×C₁₉	1	1	yes	characteristic, complemented
349	#3025	C₂×C₁₉	1	1	yes	characteristic, complemented
350	#3021	C₂×C₁₉	1	1	yes	characteristic, complemented
351	#2200	C₂×C₁₉	1	4	yes	complemented
352	#2196	C₂×C₁₉	1	4	yes	complemented
353	#2128	C₂×C₁₉	1	1	yes	characteristic, complemented
354	#2122	C₂×C₁₉	1	1	yes	characteristic, complemented
355	#2120	C₂×C₁₉	1	1	yes	characteristic, complemented
356	C₂²×C₁₉	—	2	2	no	—
357	C₂²×C₁₉	—	2	1	no	—
358	C₂²×C₁₉	—	2	1	no	—
359	C₂²×C₁₉	—	2	1	no	—
360	C₂²×C₁₉	—	4	1	no	—
361	C₂²×C₁₉	—	4	1	no	—
362	C₂²×C₁₉	—	4	1	no	—
363	C₂²×C₁₉	—	4	1	no	—
364	C₂²×C₁₉	—	4	2	no	—
365	C₂²×C₁₉	—	4	2	no	—
366	C₂²×C₁₉	—	4	2	no	—
367	C₂²×C₁₉	—	4	2	no	—
368	C₂²×C₁₉	—	4	2	no	—
369	C₂²×C₁₉	—	4	1	no	—
370	C₂²×C₁₉	—	4	2	no	—
371	C₂²×C₁₉	—	4	2	no	—
372	C₂²×C₁₉	—	4	2	no	—
373	C₂²×C₁₉	—	8	1	no	—
374	C₂²×C₁₉	—	8	2	no	—
375	C₂²×C₁₉	—	8	2	no	—
376	C₂²×C₁₉	—	8	4	no	—
377	C₂²×C₁₉	—	16	1	no	—
378	C₂²×C₁₉	—	16	4	no	—
379	C₂²×C₁₉	—	16	2	no	—
380	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
381	C₄×C₁₉	—	2	1	no	—
382	C₄×C₁₉	—	2	1	no	—
383	C₄×C₁₉	—	2	1	no	—
384	C₄×C₁₉	—	4	2	no	—
385	C₄×C₁₉	—	4	1	no	—
386	C₄×C₁₉	—	4	1	no	—
387	C₄×C₁₉	—	4	2	no	—
388	C₄×C₁₉	—	4	2	no	—
389	C₄×C₁₉	—	4	1	no	—
390	C₄×C₁₉	—	8	2	no	—
391	C₄×C₁₉	—	8	2	no	—
392	C₄×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
393	C₄×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
394	#585	C₂²×C₁₉	1	1	yes	characteristic, complemented
395	C₂×AGL(1,ℤ/8)	—	2	1	no	—
396	#560	—	2	1	no	—
397	#560	C₂²×C₁₉	1	2	yes	complemented
398	#553	—	2	1	no	—
399	#553	—	2	1	no	—
400	D₄²	—	2	1	no	—
401	D₄²	—	2	1	no	—
402	D₄²	—	2	1	no	—
403	D₄²	C₂²×C₁₉	1	2	yes	complemented
404	#540	—	2	1	no	—
405	#538	—	2	2	no	—
406	#535	—	2	1	no	—
407	#535	C₂²×C₁₉	1	1	yes	characteristic
408	#535	C₂²×C₁₉	1	1	yes	characteristic
409	#534	—	2	2	no	—
410	#525	—	2	1	no	—
411	#525	C₂²×C₁₉	1	1	yes	characteristic
412	C₂×#121	—	2	1	no	—
413	#458	—	2	1	no	—
414	#458	C₂²×C₁₉	1	2	yes	complemented
415	B(4,𝔽₂)	—	2	1	no	—
416	B(4,𝔽₂)	—	2	2	no	—
417	B(4,𝔽₂)	C₂²×C₁₉	1	2	yes	complemented
418	B(4,𝔽₂)	C₂²×C₁₉	1	4	yes	complemented
419	#454	—	2	2	no	—
420	#453	C₂²×C₁₉	1	4	yes	complemented
421	#421	—	2	1	no	—
422	#413	C₂²×C₁₉	1	1	yes	characteristic, complemented
423	#410	—	2	1	no	—
424	#410	—	2	1	no	—
425	#410	C₂²×C₁₉	1	1	yes	characteristic, complemented
426	#410	C₂²×C₁₉	1	1	yes	characteristic, complemented
427	#353	C₂²×C₁₉	1	4	yes	complemented
428	#352	C₂²×C₁₉	1	2	yes	complemented
429	AΣL(1,𝔽₁₆)	C₂²×C₁₉	1	2	yes	complemented
430	AΣL(1,𝔽₁₆)	C₂²×C₁₉	1	4	yes	complemented
431	C₂×C₁₉	—	2	1	no	—
432	C₂×C₁₉	—	4	1	no	—
433	C₂×C₁₉	—	4	1	no	—
434	C₂×C₁₉	—	4	2	no	—
435	C₂×C₁₉	—	4	1	no	—
436	C₂×C₁₉	—	8	2	no	—
437	C₂×C₁₉	—	8	2	no	—
438	C₂×C₁₉	—	8	2	no	—
439	C₂×C₁₉	C₂×B(4,𝔽₂)	1	1	yes	characteristic
440	2₋¹⁺⁴	—	2	1	no	—
441	2₋¹⁺⁴	—	4	1	no	—
442	H(5,𝔽₂)	—	2	1	no	—
443	H(5,𝔽₂)	—	2	1	no	—
444	H(5,𝔽₂)	—	4	1	no	—
445	H(5,𝔽₂)	C₂³×C₁₉	1	2	yes	—
446	C₂×#41	—	2	1	no	—
447	C₂×#41	—	2	1	no	—
448	C₂×#41	—	2	1	no	—
449	C₂×#41	—	4	2	no	—
450	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
451	C₂²×D₄	—	2	1	no	—
452	C₂²×D₄	—	2	2	no	—
453	C₂²×D₄	—	2	2	no	—
454	C₂²×D₄	—	2	2	no	—
455	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic, complemented
456	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic, complemented
457	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic, complemented
458	AGL(1,ℤ/8)	—	2	4	no	—
459	AGL(1,ℤ/8)	—	4	2	no	—
460	C₂×SD₁₆	—	4	1	no	—
461	C₂×D₈	—	4	1	no	—
462	C₂×M₁₆	—	2	1	no	—
463	#127	—	2	1	no	—
464	#127	—	2	1	no	—
465	#127	—	4	1	no	—
466	#127	C₂³×C₁₉	1	2	yes	—
467	#126	—	2	2	no	—
468	#126	—	2	2	no	—
469	#125	—	2	1	no	—
470	#124	—	2	1	no	—
471	#124	—	4	1	no	—
472	#124	D₄×C₁₉	1	2	yes	complemented
473	#123	—	2	2	no	—
474	#123	—	2	2	no	—
475	#123	—	2	2	no	—
476	#123	—	2	2	no	—
477	#123	—	2	2	no	—
478	#123	D₄×C₁₉	1	1	yes	characteristic, complemented
479	#123	C₂³×C₁₉	1	1	yes	characteristic
480	C₂²⋊Q₈	—	2	1	no	—
481	C₂²⋊Q₈	—	4	1	no	—
482	#121	—	2	2	no	—
483	#121	—	2	1	no	—
484	#121	—	2	1	no	—
485	#121	—	2	2	no	—
486	#121	—	2	2	no	—
487	#121	—	2	1	no	—
488	#121	—	2	2	no	—
489	#121	—	2	1	no	—
490	#121	—	2	1	no	—
491	#121	—	2	2	no	—
492	#121	—	2	1	no	—
493	#121	—	2	1	no	—
494	#121	—	2	2	no	—
495	#121	—	2	2	no	—
496	#121	—	2	2	no	—
497	#121	—	4	2	no	—
498	#121	—	4	1	no	—
499	#120	—	2	2	no	—
500	#120	—	2	2	no	—
501	#120	—	2	2	no	—
502	#120	—	2	1	no	—
503	#120	—	2	1	no	—
504	#120	—	2	2	no	—
505	#120	—	2	2	no	—
506	#120	—	2	4	no	—
507	#120	D₄×C₁₉	1	1	yes	characteristic, complemented
508	#120	D₄×C₁₉	1	2	yes	complemented
509	#120	C₂³×C₁₉	1	1	yes	characteristic
510	#120	C₂³×C₁₉	1	2	yes	—
511	C₄×D₄	—	2	2	no	—
512	C₄×D₄	—	2	1	no	—
513	C₄×D₄	—	2	1	no	—
514	C₄×D₄	—	2	1	no	—
515	C₄×D₄	—	2	1	no	—
516	C₄×D₄	—	2	2	no	—
517	C₄×D₄	—	4	2	no	—
518	#117	—	2	1	no	—
519	#117	—	2	1	no	—
520	#117	D₄×C₁₉	1	1	yes	characteristic, complemented
521	#117	D₄×C₁₉	1	1	yes	characteristic, complemented
522	#117	D₄×C₁₉	1	1	yes	characteristic, complemented
523	C₂×C₄⋊C₄	—	2	1	no	—
524	C₂×C₂²⋊C₄	—	2	2	no	—
525	#104	—	2	4	no	—
526	#101	—	2	1	no	—
527	#100	C₂³×C₁₉	1	2	yes	—
528	#99	—	2	1	no	—
529	#99	—	2	1	no	—
530	#99	—	2	4	no	—
531	#99	—	2	2	no	—
532	#99	—	2	2	no	—
533	#99	C₂³×C₁₉	1	2	yes	—
534	#99	C₂³×C₁₉	1	2	yes	—
535	C₁₉	#33553	1	1	yes	characteristic, direct product factor, Sylow
536	C₂⁴	—	2	2	no	—
537	C₂⁴	—	2	1	no	—
538	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
539	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
540	#41	—	2	2	no	—
541	#41	—	2	2	no	—
542	#41	—	4	1	no	—
543	#41	—	4	1	no	—
544	#41	—	4	2	no	—
545	#41	—	4	1	no	—
546	#41	—	4	1	no	—
547	#41	—	4	1	no	—
548	#41	—	4	1	no	—
549	#41	—	4	1	no	—
550	#41	—	4	2	no	—
551	#41	—	4	2	no	—
552	#41	—	4	2	no	—
553	#41	—	4	1	no	—
554	#41	—	4	1	no	—
555	#41	—	4	1	no	—
556	C₂×Q₈	—	2	1	no	—
557	C₂×Q₈	—	2	1	no	—
558	C₂×Q₈	—	2	1	no	—
559	C₂×Q₈	—	4	2	no	—
560	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
561	C₂×D₄	—	2	1	no	—
562	C₂×D₄	—	2	2	no	—
563	C₂×D₄	—	2	2	no	—
564	C₂×D₄	—	2	1	no	—
565	C₂×D₄	—	2	1	no	—
566	C₂×D₄	—	2	1	no	—
567	C₂×D₄	—	2	2	no	—
568	C₂×D₄	—	2	2	no	—
569	C₂×D₄	—	2	1	no	—
570	C₂×D₄	—	2	2	no	—
571	C₂×D₄	—	2	2	no	—
572	C₂×D₄	—	2	2	no	—
573	C₂×D₄	—	2	2	no	—
574	C₂×D₄	—	2	2	no	—
575	C₂×D₄	—	2	2	no	—
576	C₂×D₄	—	2	2	no	—
577	C₂×D₄	—	2	1	no	—
578	C₂×D₄	—	2	1	no	—
579	C₂×D₄	—	2	1	no	—
580	C₂×D₄	—	4	1	no	—
581	C₂×D₄	—	4	1	no	—
582	C₂×D₄	—	4	1	no	—
583	C₂×D₄	—	4	1	no	—
584	C₂×D₄	—	4	2	no	—
585	C₂×D₄	—	4	2	no	—
586	C₂×D₄	—	4	2	no	—
587	C₂×D₄	—	4	1	no	—
588	C₂×D₄	—	4	2	no	—
589	C₂×D₄	—	4	4	no	—
590	C₂×D₄	—	8	1	no	—
591	C₂×D₄	—	8	1	no	—
592	C₂×D₄	—	8	4	no	—
593	C₂×D₄	—	8	4	no	—
594	C₂×D₄	—	8	4	no	—
595	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
596	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
597	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
598	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
599	C₂²×C₄	—	2	2	no	—
600	C₂²×C₄	—	2	2	no	—
601	C₂²×C₄	—	2	2	no	—
602	C₂²×C₄	—	2	2	no	—
603	C₂²×C₄	—	2	2	no	—
604	C₂²×C₄	—	2	1	no	—
605	C₂²×C₄	—	2	1	no	—
606	C₂²×C₄	—	4	1	no	—
607	C₂²×C₄	—	4	1	no	—
608	C₂²×C₄	—	4	1	no	—
609	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
610	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
611	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
612	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
613	SD₁₆	—	4	4	no	—
614	D₈	—	4	4	no	—
615	M₁₆	—	2	2	no	—
616	M₁₆	—	4	1	no	—
617	C₂×C₈	—	4	1	no	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	2	2	no	—
620	C₄⋊C₄	—	2	2	no	—
621	C₄⋊C₄	—	2	1	no	—
622	C₄⋊C₄	—	2	1	no	—
623	C₄⋊C₄	—	2	1	no	—
624	C₄⋊C₄	—	2	1	no	—
625	C₄⋊C₄	—	2	1	no	—
626	C₄⋊C₄	—	4	1	no	—
627	C₄⋊C₄	—	4	1	no	—
628	C₄⋊C₄	—	4	2	no	—
629	C₂²⋊C₄	—	2	2	no	—
630	C₂²⋊C₄	—	2	2	no	—
631	C₂²⋊C₄	—	2	2	no	—
632	C₂²⋊C₄	—	2	2	no	—
633	C₂²⋊C₄	—	2	1	no	—
634	C₂²⋊C₄	—	2	1	no	—
635	C₂²⋊C₄	—	2	1	no	—
636	C₂²⋊C₄	—	2	2	no	—
637	C₂²⋊C₄	—	2	2	no	—
638	C₂²⋊C₄	—	2	1	no	—
639	C₂²⋊C₄	—	2	2	no	—
640	C₂²⋊C₄	—	2	1	no	—
641	C₂²⋊C₄	—	2	2	no	—
642	C₂²⋊C₄	—	2	2	no	—
643	C₂²⋊C₄	—	2	2	no	—
644	C₂²⋊C₄	—	4	2	no	—
645	C₂²⋊C₄	—	4	4	no	—
646	C₂²⋊C₄	—	4	2	no	—
647	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
648	C₂²⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
649	C₂²⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
650	C₄²	—	2	1	no	—
651	C₄²	—	2	1	no	—
652	C₄²	—	4	1	no	—
653	C₄²	—	4	1	no	—
654	C₄²	C₂×D₄×C₁₉	1	2	yes	—
655	C₂³	—	2	1	no	—
656	C₂³	—	2	2	no	—
657	C₂³	—	2	2	no	—
658	C₂³	—	2	2	no	—
659	C₂³	—	2	2	no	—
660	C₂³	—	4	1	no	—
661	C₂³	—	4	2	no	—
662	C₂³	—	4	1	no	—
663	C₂³	—	4	4	no	—
664	C₂³	—	4	2	no	—
665	C₂³	—	8	1	no	—
666	C₂³	—	8	2	no	—
667	C₂³	—	8	2	no	—
668	C₂³	—	8	2	no	—
669	C₂³	—	8	2	no	—
670	C₂³	C₁₉×#120	1	1	yes	characteristic
671	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
672	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
673	Q₈	—	2	2	no	—
674	Q₈	—	4	1	no	—
675	Q₈	—	4	1	no	—
676	Q₈	—	4	1	no	—
677	Q₈	—	4	1	no	—
678	D₄	—	2	2	no	—
679	D₄	—	4	1	no	—
680	D₄	—	4	1	no	—
681	D₄	—	4	1	no	—
682	D₄	—	4	2	no	—
683	D₄	—	4	1	no	—
684	D₄	—	4	1	no	—
685	D₄	—	4	2	no	—
686	D₄	—	4	2	no	—
687	D₄	—	4	2	no	—
688	D₄	—	4	2	no	—
689	D₄	—	4	4	no	—
690	D₄	—	4	4	no	—
691	D₄	—	4	2	no	—
692	D₄	—	4	2	no	—
693	D₄	—	4	1	no	—
694	D₄	—	4	1	no	—
695	D₄	—	4	1	no	—
696	D₄	—	4	1	no	—
697	D₄	—	4	1	no	—
698	D₄	—	8	1	no	—
699	D₄	—	8	2	no	—
700	D₄	—	8	2	no	—
701	D₄	—	8	2	no	—
702	D₄	—	8	2	no	—
703	D₄	—	8	2	no	—
704	D₄	—	8	2	no	—
705	D₄	—	8	2	no	—
706	D₄	—	8	4	no	—
707	D₄	—	16	4	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	2	1	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	4	2	no	—
722	C₂×C₄	—	4	2	no	—
723	C₂×C₄	—	4	2	no	—
724	C₂×C₄	—	4	1	no	—
725	C₂×C₄	—	4	2	no	—
726	C₂×C₄	—	4	1	no	—
727	C₂×C₄	—	4	1	no	—
728	C₂×C₄	—	4	1	no	—
729	C₂×C₄	—	4	2	no	—
730	C₂×C₄	—	4	2	no	—
731	C₂×C₄	—	8	1	no	—
732	C₂×C₄	—	8	2	no	—
733	C₂×C₄	—	8	2	no	—
734	C₂×C₄	—	8	2	no	—
735	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
736	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
737	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
738	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
739	C₈	—	4	2	no	—
740	C₂²	—	2	2	no	—
741	C₂²	—	2	1	no	—
742	C₂²	—	2	1	no	—
743	C₂²	—	2	1	no	—
744	C₂²	—	4	1	no	—
745	C₂²	—	4	1	no	—
746	C₂²	—	4	1	no	—
747	C₂²	—	4	1	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	4	2	no	—
750	C₂²	—	4	2	no	—
751	C₂²	—	4	2	no	—
752	C₂²	—	4	2	no	—
753	C₂²	—	4	1	no	—
754	C₂²	—	4	2	no	—
755	C₂²	—	4	2	no	—
756	C₂²	—	4	2	no	—
757	C₂²	—	8	1	no	—
758	C₂²	—	8	2	no	—
759	C₂²	—	8	2	no	—
760	C₂²	—	8	4	no	—
761	C₂²	—	16	4	no	—
762	C₂²	—	16	1	no	—
763	C₂²	—	16	2	no	—
764	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
765	C₄	—	2	1	no	—
766	C₄	—	2	1	no	—
767	C₄	—	2	1	no	—
768	C₄	—	4	1	no	—
769	C₄	—	4	1	no	—
770	C₄	—	4	2	no	—
771	C₄	—	4	2	no	—
772	C₄	—	4	2	no	—
773	C₄	—	4	1	no	—
774	C₄	—	8	2	no	—
775	C₄	—	8	2	no	—
776	C₄	C₁₉×B(4,𝔽₂)	1	1	yes	characteristic
777	C₄	C₁₉×B(4,𝔽₂)	1	1	yes	characteristic
778	C₂	—	2	1	no	—
779	C₂	—	4	1	no	—
780	C₂	—	4	1	no	—
781	C₂	—	4	2	no	—
782	C₂	—	4	1	no	—
783	C₂	—	8	2	no	—
784	C₂	—	8	2	no	—
785	C₂	—	8	2	no	—
786	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×#3537	C₂	semidirect
2. C₁₉×#3027	C₂	semidirect
3. C₁₉×#3025	C₂	semidirect
4. C₁₉×#3021	C₂	semidirect
5. C₁₉×#2200	C₂	semidirect
6. C₁₉×#2196	C₂	semidirect
7. C₁₉×#2128	C₂	semidirect
8. C₁₉×#2122	C₂	semidirect
9. C₁₉×#2120	C₂	semidirect
10. C₁₉×#585	C₂²	semidirect
13. C₁₉×#560	C₂²	semidirect
19. D₄²×C₁₉	C₂²	semidirect
30. C₁₉×#458	C₂²	semidirect
33. C₁₉×B(4,𝔽₂)	C₂²	semidirect
34. C₁₉×B(4,𝔽₂)	C₂²	semidirect
36. C₁₉×#453	C₂²	semidirect
38. C₁₉×#413	C₂²	semidirect
41. C₁₉×#410	C₂²	semidirect
42. C₁₉×#410	C₂²	semidirect
43. C₁₉×#353	C₂²	semidirect
44. C₁₉×#352	C₂²	semidirect
45. C₁₉×AΣL(1,𝔽₁₆)	C₂²	semidirect
46. C₁₉×AΣL(1,𝔽₁₆)	C₂²	semidirect
62. C₂²×D₄×C₁₉	D₄	semidirect
63. C₂²×D₄×C₁₉	D₄	semidirect
64. C₂³×C₄×C₁₉	D₄	semidirect
79. C₁₉×#124	D₄	semidirect
85. C₁₉×#123	D₄	semidirect
114. C₁₉×#120	D₄	semidirect
115. C₁₉×#120	D₄	semidirect
127. C₁₉×#117	D₄	semidirect
128. C₁₉×#117	D₄	semidirect
129. C₁₉×#117	D₄	semidirect
261. #33553	C₁₉	direct (N × H)
347. #3537	C₂×C₁₉	semidirect
348. #3027	C₂×C₁₉	semidirect
349. #3025	C₂×C₁₉	semidirect
350. #3021	C₂×C₁₉	semidirect
351. #2200	C₂×C₁₉	semidirect
352. #2196	C₂×C₁₉	semidirect
353. #2128	C₂×C₁₉	semidirect
354. #2122	C₂×C₁₉	semidirect
355. #2120	C₂×C₁₉	semidirect
394. #585	C₂²×C₁₉	semidirect
397. #560	C₂²×C₁₉	semidirect
403. D₄²	C₂²×C₁₉	semidirect
414. #458	C₂²×C₁₉	semidirect
417. B(4,𝔽₂)	C₂²×C₁₉	semidirect
418. B(4,𝔽₂)	C₂²×C₁₉	semidirect
420. #453	C₂²×C₁₉	semidirect
422. #413	C₂²×C₁₉	semidirect
425. #410	C₂²×C₁₉	semidirect
426. #410	C₂²×C₁₉	semidirect
427. #353	C₂²×C₁₉	semidirect
428. #352	C₂²×C₁₉	semidirect
429. AΣL(1,𝔽₁₆)	C₂²×C₁₉	semidirect
430. AΣL(1,𝔽₁₆)	C₂²×C₁₉	semidirect
455. C₂²×D₄	D₄×C₁₉	semidirect
456. C₂²×D₄	D₄×C₁₉	semidirect
457. C₂³×C₄	D₄×C₁₉	semidirect
472. #124	D₄×C₁₉	semidirect
478. #123	D₄×C₁₉	semidirect
507. #120	D₄×C₁₉	semidirect
508. #120	D₄×C₁₉	semidirect
520. #117	D₄×C₁₉	semidirect
521. #117	D₄×C₁₉	semidirect
522. #117	D₄×C₁₉	semidirect
535. C₁₉	#33553	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×#3537	2
C₁₉×#3027	2
C₁₉×#3025	2
C₁₉×#3021	2
C₁₉×#2200	2
C₁₉×#2196	2
C₁₉×#2128	2
C₁₉×#2122	2
C₁₉×#2120	2
#33553	19

Subgroups — C19×#33553 #18039512

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#33553 #18039512