Subgroups — C₁₉×#33568 #18039527

Order 4864.

1110 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×#3545	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3020	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#454	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2204	C₂	1	4	yes	maximal, complemented
5	C₁₉×#2203	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2202	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2133	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₉×#355	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₉×2₋¹⁺⁴	C₂²	1	1	yes	characteristic, complemented
10	C₁₉×#575	—	2	2	no	—
11	C₂×C₁₉×AGL(1,ℤ/8)	—	2	1	no	—
12	C₁₉×#563	C₂²	1	1	yes	characteristic, complemented
13	C₁₉×#562	—	2	1	no	—
14	C₁₉×H(3,𝔽₄)	C₂²	1	1	yes	characteristic, complemented
15	C₁₉×#555	C₂²	1	2	yes	complemented
16	C₁₉×#551	—	2	1	no	—
17	C₁₉×#551	—	2	2	no	—
18	C₁₉×#546	—	2	2	no	—
19	C₁₉×#542	—	2	2	no	—
20	C₁₉×#538	—	2	2	no	—
21	C₁₉×#536	C₂²	1	2	yes	—
22	C₁₉×#534	—	2	1	no	—
23	C₁₉×#529	—	2	1	no	—
24	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
25	C₁₉×#456	—	2	2	no	—
26	C₁₉×#456	C₂²	1	4	yes	complemented
27	C₁₉×#454	—	2	1	no	—
28	C₁₉×#454	—	2	1	no	—
29	C₁₉×#454	—	2	2	no	—
30	C₁₉×#454	C₂²	1	2	yes	—
31	C₁₉×#454	C₂²	1	4	yes	complemented
32	C₁₉×#454	C₂²	1	2	yes	complemented
33	C₁₉×#421	—	2	2	no	—
34	C₂×C₁₉×#104	—	2	1	no	—
35	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₁₉×#101	C₂²	1	2	yes	complemented
37	C₁₉×#356	C₂²	1	4	yes	complemented
38	C₁₉×#355	C₂²	1	2	yes	complemented
39	C₁₉×#355	C₂²	1	4	yes	complemented
40	C₁₉×#355	C₂²	1	2	yes	complemented
41	C₁₉×2₋¹⁺⁴	—	2	1	no	—
42	C₁₉×2₋¹⁺⁴	—	2	2	no	—
43	C₁₉×2₋¹⁺⁴	—	4	2	no	—
44	C₁₉×2₋¹⁺⁴	C₂³	1	2	yes	—
45	C₂×#41×C₁₉	—	2	1	no	—
46	C₂×#41×C₁₉	—	2	2	no	—
47	C₂×#41×C₁₉	—	4	1	no	—
48	C₂×#41×C₁₉	D₄	1	2	yes	—
49	C₂²×Q₈×C₁₉	—	4	1	no	—
50	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
51	C₂²×D₄×C₁₉	—	2	1	no	—
52	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
53	C₁₉×#137	—	2	4	no	—
54	C₁₉×#137	—	4	2	no	—
55	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
56	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
57	C₁₉×AGL(1,ℤ/8)	—	2	4	no	—
58	C₁₉×AGL(1,ℤ/8)	—	4	2	no	—
59	C₁₉×AGL(1,ℤ/8)	—	4	2	no	—
60	C₁₉×#135	—	4	4	no	—
61	C₂×SD₁₆×C₁₉	—	4	1	no	—
62	C₂×D₈×C₁₉	—	4	1	no	—
63	C₂×M₁₆×C₁₉	—	2	1	no	—
64	C₂×M₁₆×C₁₉	—	2	2	no	—
65	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
66	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
67	C₁₉×#126	—	2	2	no	—
68	C₁₉×#126	—	2	2	no	—
69	C₁₉×#126	—	2	2	no	—
70	C₁₉×#125	—	2	1	no	—
71	C₁₉×#124	—	2	2	no	—
72	C₁₉×#124	—	2	2	no	—
73	C₁₉×#124	—	2	1	no	—
74	C₁₉×#124	—	2	2	no	—
75	C₁₉×#124	D₄	1	1	yes	characteristic
76	C₁₉×#124	D₄	1	1	yes	characteristic
77	C₁₉×#124	D₄	1	2	yes	—
78	C₁₉×#124	C₂³	1	1	yes	characteristic
79	C₁₉×#124	C₂³	1	1	yes	characteristic
80	C₁₉×#124	C₂³	1	2	yes	—
81	C₁₉×#123	—	2	1	no	—
82	C₁₉×#123	—	2	2	no	—
83	C₁₉×#123	—	2	2	no	—
84	C₁₉×#123	—	2	2	no	—
85	C₁₉×#123	—	2	1	no	—
86	C₁₉×#123	—	2	2	no	—
87	C₁₉×#123	—	2	2	no	—
88	C₁₉×C₂²⋊Q₈	—	2	1	no	—
89	C₁₉×C₂²⋊Q₈	—	2	2	no	—
90	C₁₉×C₂²⋊Q₈	—	2	2	no	—
91	C₁₉×C₂²⋊Q₈	—	2	2	no	—
92	C₁₉×C₂²⋊Q₈	—	2	2	no	—
93	C₁₉×#121	—	2	1	no	—
94	C₁₉×#121	—	2	2	no	—
95	C₁₉×#121	—	2	2	no	—
96	C₁₉×#121	—	2	2	no	—
97	C₁₉×#121	—	2	2	no	—
98	C₁₉×#120	—	2	1	no	—
99	C₁₉×#120	—	2	2	no	—
100	C₁₉×#120	—	2	1	no	—
101	C₁₉×#120	—	2	2	no	—
102	C₄×Q₈×C₁₉	—	2	1	no	—
103	C₄×D₄×C₁₉	—	2	1	no	—
104	C₄×D₄×C₁₉	—	2	2	no	—
105	C₄×D₄×C₁₉	—	2	2	no	—
106	C₄×D₄×C₁₉	—	2	2	no	—
107	C₁₉×#117	—	2	2	no	—
108	C₁₉×#117	—	2	2	no	—
109	C₁₉×#117	D₄	1	2	yes	—
110	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
111	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
112	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
113	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
114	C₁₉×#104	—	2	2	no	—
115	C₁₉×#104	—	2	2	no	—
116	C₁₉×#104	—	2	4	no	—
117	C₁₉×#104	—	2	4	no	—
118	C₁₉×#101	—	2	1	no	—
119	C₁₉×#101	—	2	2	no	—
120	C₁₉×#101	C₂³	1	4	yes	—
121	C₁₉×#101	C₂³	1	2	yes	—
122	C₂⁴×C₁₉	—	2	1	no	—
123	C₂⁴×C₁₉	—	2	1	no	—
124	#41×C₁₉	—	2	4	no	—
125	#41×C₁₉	—	2	2	no	—
126	#41×C₁₉	—	2	2	no	—
127	#41×C₁₉	—	2	4	no	—
128	#41×C₁₉	—	4	2	no	—
129	#41×C₁₉	—	4	1	no	—
130	#41×C₁₉	—	4	2	no	—
131	#41×C₁₉	—	4	2	no	—
132	#41×C₁₉	—	4	2	no	—
133	#41×C₁₉	—	4	2	no	—
134	#41×C₁₉	—	4	4	no	—
135	#41×C₁₉	—	4	1	no	—
136	#41×C₁₉	—	4	2	no	—
137	C₂×Q₈×C₁₉	—	2	1	no	—
138	C₂×Q₈×C₁₉	—	2	1	no	—
139	C₂×Q₈×C₁₉	—	2	2	no	—
140	C₂×Q₈×C₁₉	—	4	1	no	—
141	C₂×Q₈×C₁₉	—	4	1	no	—
142	C₂×Q₈×C₁₉	—	4	2	no	—
143	C₂×Q₈×C₁₉	—	4	2	no	—
144	C₂×Q₈×C₁₉	—	4	4	no	—
145	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
146	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
147	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
148	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
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	2	no	—
153	C₂×D₄×C₁₉	—	2	2	no	—
154	C₂×D₄×C₁₉	—	2	1	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	—	4	1	no	—
159	C₂×D₄×C₁₉	—	4	1	no	—
160	C₂×D₄×C₁₉	—	8	1	no	—
161	C₂×D₄×C₁₉	—	8	1	no	—
162	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
163	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
164	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₉	—	2	2	no	—
166	C₂²×C₄×C₁₉	—	2	2	no	—
167	C₂²×C₄×C₁₉	—	2	1	no	—
168	C₂²×C₄×C₁₉	—	2	1	no	—
169	C₂²×C₄×C₁₉	—	2	2	no	—
170	C₂²×C₄×C₁₉	—	4	1	no	—
171	C₂²×C₄×C₁₉	—	4	2	no	—
172	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
174	Q₁₆×C₁₉	—	4	4	no	—
175	SD₁₆×C₁₉	—	4	4	no	—
176	SD₁₆×C₁₉	—	4	2	no	—
177	SD₁₆×C₁₉	—	4	2	no	—
178	SD₁₆×C₁₉	—	4	4	no	—
179	D₈×C₁₉	—	4	2	no	—
180	D₈×C₁₉	—	4	2	no	—
181	D₈×C₁₉	—	4	4	no	—
182	M₁₆×C₁₉	—	2	2	no	—
183	M₁₆×C₁₉	—	2	4	no	—
184	M₁₆×C₁₉	—	4	1	no	—
185	M₁₆×C₁₉	—	4	2	no	—
186	C₂×C₈×C₁₉	—	4	1	no	—
187	C₂×C₈×C₁₉	—	4	2	no	—
188	C₄⋊C₄×C₁₉	—	2	2	no	—
189	C₄⋊C₄×C₁₉	—	2	2	no	—
190	C₄⋊C₄×C₁₉	—	2	1	no	—
191	C₄⋊C₄×C₁₉	—	2	1	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	—	2	2	no	—
197	C₂²⋊C₄×C₁₉	—	2	2	no	—
198	C₂²⋊C₄×C₁₉	—	2	2	no	—
199	C₂²⋊C₄×C₁₉	—	2	1	no	—
200	C₂²⋊C₄×C₁₉	—	2	1	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	—	2	2	no	—
212	C₄²×C₁₉	—	2	2	no	—
213	C₄²×C₁₉	—	2	1	no	—
214	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
215	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
216	C₄²×C₁₉	C₂×D₄	1	2	yes	—
217	C₄²×C₁₉	C₂×D₄	1	2	yes	—
218	#33568	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
219	C₂³×C₁₉	—	2	1	no	—
220	C₂³×C₁₉	—	2	1	no	—
221	C₂³×C₁₉	—	2	2	no	—
222	C₂³×C₁₉	—	4	1	no	—
223	C₂³×C₁₉	—	4	1	no	—
224	C₂³×C₁₉	—	4	1	no	—
225	C₂³×C₁₉	—	8	1	no	—
226	C₂³×C₁₉	—	8	2	no	—
227	C₂³×C₁₉	—	8	2	no	—
228	C₂³×C₁₉	#120	1	1	yes	characteristic
229	Q₈×C₁₉	—	2	2	no	—
230	Q₈×C₁₉	—	2	4	no	—
231	Q₈×C₁₉	—	4	1	no	—
232	Q₈×C₁₉	—	4	2	no	—
233	Q₈×C₁₉	—	4	1	no	—
234	Q₈×C₁₉	—	4	2	no	—
235	Q₈×C₁₉	—	4	2	no	—
236	Q₈×C₁₉	—	4	1	no	—
237	Q₈×C₁₉	—	8	1	no	—
238	D₄×C₁₉	—	2	2	no	—
239	D₄×C₁₉	—	2	4	no	—
240	D₄×C₁₉	—	4	1	no	—
241	D₄×C₁₉	—	4	1	no	—
242	D₄×C₁₉	—	4	2	no	—
243	D₄×C₁₉	—	4	2	no	—
244	D₄×C₁₉	—	4	1	no	—
245	D₄×C₁₉	—	4	2	no	—
246	D₄×C₁₉	—	4	2	no	—
247	D₄×C₁₉	—	4	2	no	—
248	D₄×C₁₉	—	4	2	no	—
249	D₄×C₁₉	—	8	1	no	—
250	D₄×C₁₉	—	8	2	no	—
251	D₄×C₁₉	—	8	2	no	—
252	D₄×C₁₉	—	8	1	no	—
253	D₄×C₁₉	—	8	2	no	—
254	C₂×C₄×C₁₉	—	2	1	no	—
255	C₂×C₄×C₁₉	—	2	2	no	—
256	C₂×C₄×C₁₉	—	2	2	no	—
257	C₂×C₄×C₁₉	—	2	1	no	—
258	C₂×C₄×C₁₉	—	2	1	no	—
259	C₂×C₄×C₁₉	—	2	2	no	—
260	C₂×C₄×C₁₉	—	2	1	no	—
261	C₂×C₄×C₁₉	—	2	2	no	—
262	C₂×C₄×C₁₉	—	2	2	no	—
263	C₂×C₄×C₁₉	—	4	2	no	—
264	C₂×C₄×C₁₉	—	4	4	no	—
265	C₂×C₄×C₁₉	—	4	4	no	—
266	C₂×C₄×C₁₉	—	4	2	no	—
267	C₂×C₄×C₁₉	—	4	1	no	—
268	C₂×C₄×C₁₉	—	8	2	no	—
269	C₂×C₄×C₁₉	—	8	2	no	—
270	C₂×C₄×C₁₉	—	8	1	no	—
271	C₂×C₄×C₁₉	—	8	2	no	—
272	C₂×C₄×C₁₉	—	8	1	no	—
273	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
274	C₂×C₄×C₁₉	#120	1	2	yes	—
275	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
276	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
277	C₈×C₁₉	—	4	2	no	—
278	C₈×C₁₉	—	4	4	no	—
279	#3545	C₂×C₁₉	1	1	yes	characteristic, complemented
280	#3020	C₂×C₁₉	1	2	yes	complemented
281	C₂×#454	C₂×C₁₉	1	1	yes	characteristic, complemented
282	#2204	C₂×C₁₉	1	4	yes	complemented
283	#2203	C₂×C₁₉	1	2	yes	complemented
284	#2202	C₂×C₁₉	1	2	yes	complemented
285	#2133	C₂×C₁₉	1	2	yes	complemented
286	C₂×#355	C₂×C₁₉	1	1	yes	characteristic, complemented
287	C₂²×C₁₉	—	4	1	no	—
288	C₂²×C₁₉	—	4	2	no	—
289	C₂²×C₁₉	—	4	2	no	—
290	C₂²×C₁₉	—	4	2	no	—
291	C₂²×C₁₉	—	4	2	no	—
292	C₂²×C₁₉	—	4	2	no	—
293	C₂²×C₁₉	—	4	2	no	—
294	C₂²×C₁₉	—	4	1	no	—
295	C₂²×C₁₉	—	4	1	no	—
296	C₂²×C₁₉	—	8	2	no	—
297	C₂²×C₁₉	—	16	1	no	—
298	C₂²×C₁₉	—	16	1	no	—
299	C₂²×C₁₉	—	16	2	no	—
300	C₂²×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
301	C₂²×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
302	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
303	C₄×C₁₉	—	2	1	no	—
304	C₄×C₁₉	—	2	2	no	—
305	C₄×C₁₉	—	2	2	no	—
306	C₄×C₁₉	—	2	1	no	—
307	C₄×C₁₉	—	4	1	no	—
308	C₄×C₁₉	—	4	2	no	—
309	C₄×C₁₉	—	4	2	no	—
310	C₄×C₁₉	—	4	1	no	—
311	C₄×C₁₉	—	4	2	no	—
312	C₄×C₁₉	—	4	2	no	—
313	C₂×2₋¹⁺⁴	C₂²×C₁₉	1	1	yes	characteristic, complemented
314	#575	—	2	2	no	—
315	C₂×AGL(1,ℤ/8)	—	2	1	no	—
316	#563	C₂²×C₁₉	1	1	yes	characteristic, complemented
317	#562	—	2	1	no	—
318	H(3,𝔽₄)	C₂²×C₁₉	1	1	yes	characteristic, complemented
319	#555	C₂²×C₁₉	1	2	yes	complemented
320	#551	—	2	1	no	—
321	#551	—	2	2	no	—
322	#546	—	2	2	no	—
323	#542	—	2	2	no	—
324	#538	—	2	2	no	—
325	#536	C₂²×C₁₉	1	2	yes	—
326	#534	—	2	1	no	—
327	#529	—	2	1	no	—
328	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
329	#456	—	2	2	no	—
330	#456	C₂²×C₁₉	1	4	yes	complemented
331	#454	—	2	1	no	—
332	#454	—	2	1	no	—
333	#454	—	2	2	no	—
334	#454	C₂²×C₁₉	1	2	yes	—
335	#454	C₂²×C₁₉	1	4	yes	complemented
336	#454	C₂²×C₁₉	1	2	yes	complemented
337	#421	—	2	2	no	—
338	C₂×#104	—	2	1	no	—
339	C₂×#101	C₂²×C₁₉	1	2	yes	complemented
340	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic, complemented
341	#356	C₂²×C₁₉	1	4	yes	complemented
342	#355	C₂²×C₁₉	1	2	yes	complemented
343	#355	C₂²×C₁₉	1	2	yes	complemented
344	#355	C₂²×C₁₉	1	4	yes	complemented
345	C₂×C₁₉	—	2	1	no	—
346	C₂×C₁₉	—	2	1	no	—
347	C₂×C₁₉	—	2	1	no	—
348	C₂×C₁₉	—	8	1	no	—
349	C₂×C₁₉	—	8	2	no	—
350	C₂×C₁₉	—	8	1	no	—
351	C₂×C₁₉	—	8	2	no	—
352	C₂×C₁₉	C₂×B(4,𝔽₂)	1	1	yes	characteristic
353	2₋¹⁺⁴	—	2	1	no	—
354	2₋¹⁺⁴	—	2	2	no	—
355	2₋¹⁺⁴	—	4	2	no	—
356	2₋¹⁺⁴	C₂³×C₁₉	1	2	yes	—
357	C₂×#41	—	2	1	no	—
358	C₂×#41	—	2	2	no	—
359	C₂×#41	—	4	1	no	—
360	C₂×#41	D₄×C₁₉	1	2	yes	—
361	C₂²×Q₈	—	4	1	no	—
362	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
363	C₂²×D₄	—	2	1	no	—
364	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
365	#137	—	2	4	no	—
366	#137	—	4	2	no	—
367	AGL(1,ℤ/8)	—	2	2	no	—
368	AGL(1,ℤ/8)	—	2	2	no	—
369	AGL(1,ℤ/8)	—	2	4	no	—
370	AGL(1,ℤ/8)	—	4	2	no	—
371	AGL(1,ℤ/8)	—	4	2	no	—
372	#135	—	4	4	no	—
373	C₂×SD₁₆	—	4	1	no	—
374	C₂×D₈	—	4	1	no	—
375	C₂×M₁₆	—	2	1	no	—
376	C₂×M₁₆	—	2	2	no	—
377	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
378	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
379	#126	—	2	2	no	—
380	#126	—	2	2	no	—
381	#126	—	2	2	no	—
382	#125	—	2	1	no	—
383	#124	—	2	2	no	—
384	#124	—	2	2	no	—
385	#124	—	2	1	no	—
386	#124	—	2	2	no	—
387	#124	D₄×C₁₉	1	1	yes	characteristic
388	#124	D₄×C₁₉	1	1	yes	characteristic
389	#124	D₄×C₁₉	1	2	yes	—
390	#124	C₂³×C₁₉	1	1	yes	characteristic
391	#124	C₂³×C₁₉	1	1	yes	characteristic
392	#124	C₂³×C₁₉	1	2	yes	—
393	#123	—	2	1	no	—
394	#123	—	2	2	no	—
395	#123	—	2	2	no	—
396	#123	—	2	2	no	—
397	#123	—	2	1	no	—
398	#123	—	2	2	no	—
399	#123	—	2	2	no	—
400	C₂²⋊Q₈	—	2	1	no	—
401	C₂²⋊Q₈	—	2	2	no	—
402	C₂²⋊Q₈	—	2	2	no	—
403	C₂²⋊Q₈	—	2	2	no	—
404	C₂²⋊Q₈	—	2	2	no	—
405	#121	—	2	1	no	—
406	#121	—	2	2	no	—
407	#121	—	2	2	no	—
408	#121	—	2	2	no	—
409	#121	—	2	2	no	—
410	#120	—	2	1	no	—
411	#120	—	2	2	no	—
412	#120	—	2	1	no	—
413	#120	—	2	2	no	—
414	C₄×Q₈	—	2	1	no	—
415	C₄×D₄	—	2	1	no	—
416	C₄×D₄	—	2	2	no	—
417	C₄×D₄	—	2	2	no	—
418	C₄×D₄	—	2	2	no	—
419	#117	—	2	2	no	—
420	#117	—	2	2	no	—
421	#117	D₄×C₁₉	1	2	yes	—
422	C₂×C₂²⋊C₄	—	2	1	no	—
423	C₂×C₂²⋊C₄	—	2	2	no	—
424	C₂×C₂²⋊C₄	—	2	2	no	—
425	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
426	#104	—	2	2	no	—
427	#104	—	2	2	no	—
428	#104	—	2	4	no	—
429	#104	—	2	4	no	—
430	#101	—	2	1	no	—
431	#101	—	2	2	no	—
432	#101	C₂³×C₁₉	1	4	yes	—
433	#101	C₂³×C₁₉	1	2	yes	—
434	C₁₉	#33568	1	1	yes	characteristic, direct product factor, Sylow
435	C₂⁴	—	2	1	no	—
436	C₂⁴	—	2	1	no	—
437	#41	—	2	4	no	—
438	#41	—	2	2	no	—
439	#41	—	2	2	no	—
440	#41	—	2	4	no	—
441	#41	—	4	2	no	—
442	#41	—	4	1	no	—
443	#41	—	4	2	no	—
444	#41	—	4	2	no	—
445	#41	—	4	2	no	—
446	#41	—	4	2	no	—
447	#41	—	4	4	no	—
448	#41	—	4	1	no	—
449	#41	—	4	2	no	—
450	C₂×Q₈	—	2	1	no	—
451	C₂×Q₈	—	2	1	no	—
452	C₂×Q₈	—	2	2	no	—
453	C₂×Q₈	—	4	1	no	—
454	C₂×Q₈	—	4	1	no	—
455	C₂×Q₈	—	4	2	no	—
456	C₂×Q₈	—	4	2	no	—
457	C₂×Q₈	—	4	4	no	—
458	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
459	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
460	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
461	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
462	C₂×D₄	—	2	1	no	—
463	C₂×D₄	—	2	2	no	—
464	C₂×D₄	—	2	2	no	—
465	C₂×D₄	—	2	2	no	—
466	C₂×D₄	—	2	2	no	—
467	C₂×D₄	—	2	1	no	—
468	C₂×D₄	—	2	2	no	—
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	—	4	1	no	—
471	C₂×D₄	—	4	1	no	—
472	C₂×D₄	—	4	1	no	—
473	C₂×D₄	—	8	1	no	—
474	C₂×D₄	—	8	1	no	—
475	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
476	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
477	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	2	no	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	2	1	no	—
482	C₂²×C₄	—	2	2	no	—
483	C₂²×C₄	—	4	1	no	—
484	C₂²×C₄	—	4	2	no	—
485	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
486	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
487	Q₁₆	—	4	4	no	—
488	SD₁₆	—	4	4	no	—
489	SD₁₆	—	4	2	no	—
490	SD₁₆	—	4	2	no	—
491	SD₁₆	—	4	4	no	—
492	D₈	—	4	2	no	—
493	D₈	—	4	2	no	—
494	D₈	—	4	4	no	—
495	M₁₆	—	2	2	no	—
496	M₁₆	—	2	4	no	—
497	M₁₆	—	4	1	no	—
498	M₁₆	—	4	2	no	—
499	C₂×C₈	—	4	1	no	—
500	C₂×C₈	—	4	2	no	—
501	C₄⋊C₄	—	2	2	no	—
502	C₄⋊C₄	—	2	2	no	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	2	2	no	—
506	C₄⋊C₄	—	2	2	no	—
507	C₄⋊C₄	—	2	2	no	—
508	C₄⋊C₄	—	2	2	no	—
509	C₄⋊C₄	—	2	2	no	—
510	C₂²⋊C₄	—	2	2	no	—
511	C₂²⋊C₄	—	2	2	no	—
512	C₂²⋊C₄	—	2	1	no	—
513	C₂²⋊C₄	—	2	1	no	—
514	C₂²⋊C₄	—	2	2	no	—
515	C₂²⋊C₄	—	2	2	no	—
516	C₂²⋊C₄	—	2	2	no	—
517	C₂²⋊C₄	—	2	2	no	—
518	C₂²⋊C₄	—	2	2	no	—
519	C₂²⋊C₄	—	2	2	no	—
520	C₂²⋊C₄	—	2	2	no	—
521	C₂²⋊C₄	—	2	2	no	—
522	C₂²⋊C₄	—	2	2	no	—
523	C₂²⋊C₄	—	2	2	no	—
524	C₂²⋊C₄	—	2	2	no	—
525	C₄²	—	2	2	no	—
526	C₄²	—	2	1	no	—
527	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
528	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
529	C₄²	C₂×D₄×C₁₉	1	2	yes	—
530	C₄²	C₂×D₄×C₁₉	1	2	yes	—
531	C₂³	—	2	1	no	—
532	C₂³	—	2	1	no	—
533	C₂³	—	2	2	no	—
534	C₂³	—	4	1	no	—
535	C₂³	—	4	1	no	—
536	C₂³	—	4	1	no	—
537	C₂³	—	8	1	no	—
538	C₂³	—	8	2	no	—
539	C₂³	—	8	2	no	—
540	C₂³	C₁₉×#120	1	1	yes	characteristic
541	Q₈	—	2	2	no	—
542	Q₈	—	2	4	no	—
543	Q₈	—	4	1	no	—
544	Q₈	—	4	2	no	—
545	Q₈	—	4	1	no	—
546	Q₈	—	4	2	no	—
547	Q₈	—	4	2	no	—
548	Q₈	—	4	1	no	—
549	Q₈	—	8	1	no	—
550	D₄	—	2	2	no	—
551	D₄	—	2	4	no	—
552	D₄	—	4	1	no	—
553	D₄	—	4	1	no	—
554	D₄	—	4	2	no	—
555	D₄	—	4	2	no	—
556	D₄	—	4	1	no	—
557	D₄	—	4	2	no	—
558	D₄	—	4	2	no	—
559	D₄	—	4	2	no	—
560	D₄	—	4	2	no	—
561	D₄	—	8	1	no	—
562	D₄	—	8	2	no	—
563	D₄	—	8	2	no	—
564	D₄	—	8	2	no	—
565	D₄	—	8	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	4	2	no	—
576	C₂×C₄	—	4	4	no	—
577	C₂×C₄	—	4	4	no	—
578	C₂×C₄	—	4	2	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	8	2	no	—
581	C₂×C₄	—	8	1	no	—
582	C₂×C₄	—	8	2	no	—
583	C₂×C₄	—	8	1	no	—
584	C₂×C₄	—	8	2	no	—
585	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
586	C₂×C₄	C₁₉×#120	1	2	yes	—
587	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
588	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
589	C₈	—	4	2	no	—
590	C₈	—	4	4	no	—
591	C₂²	—	4	1	no	—
592	C₂²	—	4	2	no	—
593	C₂²	—	4	2	no	—
594	C₂²	—	4	2	no	—
595	C₂²	—	4	2	no	—
596	C₂²	—	4	2	no	—
597	C₂²	—	4	2	no	—
598	C₂²	—	4	1	no	—
599	C₂²	—	4	1	no	—
600	C₂²	—	8	2	no	—
601	C₂²	—	16	1	no	—
602	C₂²	—	16	1	no	—
603	C₂²	—	16	2	no	—
604	C₂²	C₁₉×B(4,𝔽₂)	1	1	yes	characteristic
605	C₂²	C₁₉×B(4,𝔽₂)	1	1	yes	characteristic
606	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
607	C₄	—	2	1	no	—
608	C₄	—	2	2	no	—
609	C₄	—	2	2	no	—
610	C₄	—	2	1	no	—
611	C₄	—	4	1	no	—
612	C₄	—	4	2	no	—
613	C₄	—	4	2	no	—
614	C₄	—	4	1	no	—
615	C₄	—	4	2	no	—
616	C₄	—	4	2	no	—
617	C₂	—	2	1	no	—
618	C₂	—	2	1	no	—
619	C₂	—	2	1	no	—
620	C₂	—	8	1	no	—
621	C₂	—	8	1	no	—
622	C₂	—	8	2	no	—
623	C₂	—	8	2	no	—
624	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×Q₈	C₂⁴×C₁₉
LCS	G ▷ C₂×Q₈ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂³×C₁₉ ◁ C₂²×Q₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3545	C₂	semidirect
2. C₁₉×#3020	C₂	semidirect
3. C₂×C₁₉×#454	C₂	semidirect
4. C₁₉×#2204	C₂	semidirect
5. C₁₉×#2203	C₂	semidirect
6. C₁₉×#2202	C₂	semidirect
7. C₁₉×#2133	C₂	semidirect
8. C₂×C₁₉×#355	C₂	semidirect
9. C₂×C₁₉×2₋¹⁺⁴	C₂²	semidirect
12. C₁₉×#563	C₂²	semidirect
14. C₁₉×H(3,𝔽₄)	C₂²	semidirect
15. C₁₉×#555	C₂²	semidirect
26. C₁₉×#456	C₂²	semidirect
31. C₁₉×#454	C₂²	semidirect
32. C₁₉×#454	C₂²	semidirect
35. C₂×C₁₉×#101	C₂²	semidirect
36. C₂×C₁₉×#101	C₂²	semidirect
37. C₁₉×#356	C₂²	semidirect
38. C₁₉×#355	C₂²	semidirect
39. C₁₉×#355	C₂²	semidirect
40. C₁₉×#355	C₂²	semidirect
218. #33568	C₁₉	direct (N × H)
279. #3545	C₂×C₁₉	semidirect
280. #3020	C₂×C₁₉	semidirect
281. C₂×#454	C₂×C₁₉	semidirect
282. #2204	C₂×C₁₉	semidirect
283. #2203	C₂×C₁₉	semidirect
284. #2202	C₂×C₁₉	semidirect
285. #2133	C₂×C₁₉	semidirect
286. C₂×#355	C₂×C₁₉	semidirect
313. C₂×2₋¹⁺⁴	C₂²×C₁₉	semidirect
316. #563	C₂²×C₁₉	semidirect
318. H(3,𝔽₄)	C₂²×C₁₉	semidirect
319. #555	C₂²×C₁₉	semidirect
330. #456	C₂²×C₁₉	semidirect
335. #454	C₂²×C₁₉	semidirect
336. #454	C₂²×C₁₉	semidirect
339. C₂×#101	C₂²×C₁₉	semidirect
340. C₂×#101	C₂²×C₁₉	semidirect
341. #356	C₂²×C₁₉	semidirect
342. #355	C₂²×C₁₉	semidirect
343. #355	C₂²×C₁₉	semidirect
344. #355	C₂²×C₁₉	semidirect
434. C₁₉	#33568	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×#3545	2
C₁₉×#3020	2
C₂×C₁₉×#454	2
C₁₉×#2204	2
C₁₉×#2203	2
C₁₉×#2202	2
C₁₉×#2133	2
C₂×C₁₉×#355	2
#33568	19

Subgroups — C19×#33568 #18039527

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#33568 #18039527