Subgroups — C₁₉×#33570 #18039529

Order 4864.

1212 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3549	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3021	C₂	1	2	yes	maximal, complemented
3	C₁₉×#3018	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2204	C₂	1	4	yes	maximal, complemented
5	C₁₉×#2202	C₂	1	4	yes	maximal, complemented
6	C₁₉×#2134	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2132	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#585	C₂²	1	1	yes	characteristic, complemented
9	C₁₉×#575	—	2	1	no	—
10	C₂×C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
11	C₁₉×H(3,𝔽₄)	—	2	1	no	—
12	C₁₉×H(3,𝔽₄)	C₂²	1	2	yes	complemented
13	C₁₉×#555	—	2	2	no	—
14	C₁₉×#555	C₂²	1	2	yes	complemented
15	D₄²×C₁₉	—	2	2	no	—
16	D₄²×C₁₉	—	2	1	no	—
17	C₁₉×#535	—	2	1	no	—
18	C₁₉×#535	—	2	4	no	—
19	C₁₉×#535	C₂²	1	2	yes	—
20	C₁₉×#532	—	2	1	no	—
21	C₁₉×#532	C₂²	1	1	yes	characteristic
22	C₁₉×#456	C₂²	1	2	yes	complemented
23	C₁₉×#455	—	2	1	no	—
24	C₁₉×#454	C₂²	1	2	yes	complemented
25	C₁₉×#454	C₂²	1	8	yes	complemented
26	C₁₉×#453	—	2	1	no	—
27	C₁₉×#453	—	2	4	no	—
28	C₁₉×#421	—	2	2	no	—
29	C₂×C₁₉×#104	—	2	1	no	—
30	C₁₉×#413	C₂²	1	1	yes	characteristic, complemented
31	C₁₉×#413	C₂²	1	2	yes	complemented
32	C₁₉×#356	C₂²	1	2	yes	complemented
33	C₁₉×#355	C₂²	1	2	yes	complemented
34	C₁₉×#355	C₂²	1	8	yes	complemented
35	C₁₉×2₋¹⁺⁴	—	4	1	no	—
36	C₁₉×2₋¹⁺⁴	C₂³	1	2	yes	—
37	C₁₉×H(5,𝔽₂)	—	2	2	no	—
38	C₁₉×H(5,𝔽₂)	—	2	1	no	—
39	C₁₉×H(5,𝔽₂)	—	4	1	no	—
40	C₂×#41×C₁₉	—	2	2	no	—
41	C₂×#41×C₁₉	—	2	1	no	—
42	C₂×#41×C₁₉	—	2	2	no	—
43	C₂×#41×C₁₉	—	4	2	no	—
44	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
45	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₁₉	—	2	4	no	—
47	C₂²×D₄×C₁₉	—	2	1	no	—
48	C₂²×D₄×C₁₉	D₄	1	2	yes	—
49	C₁₉×#137	—	2	2	no	—
50	C₁₉×#137	—	4	1	no	—
51	C₁₉×AGL(1,ℤ/8)	—	2	8	no	—
52	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
53	C₁₉×AGL(1,ℤ/8)	—	4	1	no	—
54	C₁₉×AGL(1,ℤ/8)	—	4	4	no	—
55	C₁₉×#135	—	4	2	no	—
56	C₂×SD₁₆×C₁₉	—	4	2	no	—
57	C₂×D₈×C₁₉	—	4	2	no	—
58	C₂×M₁₆×C₁₉	—	2	1	no	—
59	C₂×M₁₆×C₁₉	—	2	2	no	—
60	C₁₉×C₄⋊Q₈	—	2	1	no	—
61	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
62	C₁₉×#127	—	2	1	no	—
63	C₁₉×#127	—	2	2	no	—
64	C₁₉×#127	D₄	1	1	yes	characteristic
65	C₁₉×#127	D₄	1	4	yes	—
66	C₁₉×#124	—	2	4	no	—
67	C₁₉×#124	—	2	2	no	—
68	C₁₉×#124	—	2	2	no	—
69	C₁₉×#124	—	2	4	no	—
70	C₁₉×#124	D₄	1	1	yes	characteristic
71	C₁₉×#124	C₂³	1	1	yes	characteristic
72	C₁₉×#124	C₂³	1	4	yes	—
73	C₁₉×#121	—	2	2	no	—
74	C₁₉×#121	—	2	2	no	—
75	C₁₉×#121	—	2	4	no	—
76	C₁₉×#121	—	2	2	no	—
77	C₁₉×#121	—	2	4	no	—
78	C₁₉×#121	—	2	2	no	—
79	C₁₉×#121	—	2	2	no	—
80	C₁₉×#120	—	2	2	no	—
81	C₁₉×#120	—	2	4	no	—
82	C₁₉×#120	—	2	2	no	—
83	C₁₉×#120	—	2	2	no	—
84	C₁₉×#120	—	2	4	no	—
85	C₁₉×#120	—	2	2	no	—
86	C₄×D₄×C₁₉	—	2	2	no	—
87	C₄×D₄×C₁₉	—	2	2	no	—
88	C₄×D₄×C₁₉	—	2	2	no	—
89	C₁₉×#117	—	2	1	no	—
90	C₁₉×#117	—	2	4	no	—
91	C₁₉×#117	D₄	1	2	yes	—
92	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
93	C₁₉×#104	—	2	2	no	—
94	C₁₉×#104	—	2	2	no	—
95	C₁₉×#104	—	2	8	no	—
96	C₁₉×#101	C₂³	1	2	yes	—
97	C₁₉×#101	C₂³	1	4	yes	—
98	C₁₉×#100	—	2	2	no	—
99	C₁₉×#100	—	2	1	no	—
100	C₂⁴×C₁₉	—	2	2	no	—
101	C₂⁴×C₁₉	—	2	2	no	—
102	#41×C₁₉	—	2	2	no	—
103	#41×C₁₉	—	2	4	no	—
104	#41×C₁₉	—	2	4	no	—
105	#41×C₁₉	—	2	2	no	—
106	#41×C₁₉	—	4	1	no	—
107	#41×C₁₉	—	4	1	no	—
108	#41×C₁₉	—	4	2	no	—
109	#41×C₁₉	—	4	1	no	—
110	#41×C₁₉	—	4	1	no	—
111	#41×C₁₉	—	4	1	no	—
112	#41×C₁₉	—	4	2	no	—
113	#41×C₁₉	—	4	4	no	—
114	#41×C₁₉	—	4	2	no	—
115	#41×C₁₉	—	4	1	no	—
116	#41×C₁₉	—	8	4	no	—
117	C₂×Q₈×C₁₉	—	2	2	no	—
118	C₂×Q₈×C₁₉	—	2	2	no	—
119	C₂×Q₈×C₁₉	—	2	1	no	—
120	C₂×Q₈×C₁₉	—	4	2	no	—
121	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
122	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
123	C₂×D₄×C₁₉	—	2	2	no	—
124	C₂×D₄×C₁₉	—	2	1	no	—
125	C₂×D₄×C₁₉	—	2	2	no	—
126	C₂×D₄×C₁₉	—	2	2	no	—
127	C₂×D₄×C₁₉	—	2	2	no	—
128	C₂×D₄×C₁₉	—	2	2	no	—
129	C₂×D₄×C₁₉	—	2	4	no	—
130	C₂×D₄×C₁₉	—	2	4	no	—
131	C₂×D₄×C₁₉	—	2	1	no	—
132	C₂×D₄×C₁₉	—	2	4	no	—
133	C₂×D₄×C₁₉	—	2	2	no	—
134	C₂×D₄×C₁₉	—	4	2	no	—
135	C₂×D₄×C₁₉	—	4	2	no	—
136	C₂×D₄×C₁₉	—	4	4	no	—
137	C₂×D₄×C₁₉	—	4	2	no	—
138	C₂×D₄×C₁₉	—	4	2	no	—
139	C₂×D₄×C₁₉	—	4	1	no	—
140	C₂×D₄×C₁₉	—	8	8	no	—
141	C₂×D₄×C₁₉	—	8	1	no	—
142	C₂×D₄×C₁₉	—	8	1	no	—
143	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
144	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
145	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
146	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₁₉	—	2	4	no	—
148	C₂²×C₄×C₁₉	—	2	1	no	—
149	C₂²×C₄×C₁₉	—	2	1	no	—
150	C₂²×C₄×C₁₉	—	4	1	no	—
151	C₂²×C₄×C₁₉	—	4	2	no	—
152	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
154	Q₁₆×C₁₉	—	4	2	no	—
155	SD₁₆×C₁₉	—	4	2	no	—
156	SD₁₆×C₁₉	—	4	8	no	—
157	SD₁₆×C₁₉	—	4	2	no	—
158	D₈×C₁₉	—	4	8	no	—
159	D₈×C₁₉	—	4	2	no	—
160	M₁₆×C₁₉	—	2	4	no	—
161	M₁₆×C₁₉	—	2	2	no	—
162	M₁₆×C₁₉	—	4	2	no	—
163	M₁₆×C₁₉	—	4	1	no	—
164	C₂×C₈×C₁₉	—	4	2	no	—
165	C₂×C₈×C₁₉	—	4	1	no	—
166	C₄⋊C₄×C₁₉	—	2	2	no	—
167	C₄⋊C₄×C₁₉	—	2	2	no	—
168	C₄⋊C₄×C₁₉	—	2	2	no	—
169	C₂²⋊C₄×C₁₉	—	2	4	no	—
170	C₂²⋊C₄×C₁₉	—	2	2	no	—
171	C₂²⋊C₄×C₁₉	—	2	4	no	—
172	C₂²⋊C₄×C₁₉	—	2	2	no	—
173	C₂²⋊C₄×C₁₉	—	2	2	no	—
174	C₂²⋊C₄×C₁₉	—	2	4	no	—
175	C₂²⋊C₄×C₁₉	—	2	2	no	—
176	C₂²⋊C₄×C₁₉	—	2	4	no	—
177	C₄²×C₁₉	—	2	2	no	—
178	C₄²×C₁₉	—	2	1	no	—
179	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
181	C₄²×C₁₉	C₂×D₄	1	4	yes	—
182	#33570	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
183	C₂³×C₁₉	—	2	4	no	—
184	C₂³×C₁₉	—	2	1	no	—
185	C₂³×C₁₉	—	4	1	no	—
186	C₂³×C₁₉	—	4	2	no	—
187	C₂³×C₁₉	—	8	2	no	—
188	C₂³×C₁₉	—	8	4	no	—
189	C₂³×C₁₉	—	8	4	no	—
190	C₂³×C₁₉	—	8	2	no	—
191	C₂³×C₁₉	#120	1	2	yes	—
192	C₂³×C₁₉	#120	1	1	yes	characteristic
193	Q₈×C₁₉	—	2	4	no	—
194	Q₈×C₁₉	—	2	2	no	—
195	Q₈×C₁₉	—	4	1	no	—
196	Q₈×C₁₉	—	4	1	no	—
197	Q₈×C₁₉	—	4	1	no	—
198	Q₈×C₁₉	—	8	2	no	—
199	D₄×C₁₉	—	2	4	no	—
200	D₄×C₁₉	—	2	2	no	—
201	D₄×C₁₉	—	4	2	no	—
202	D₄×C₁₉	—	4	1	no	—
203	D₄×C₁₉	—	4	4	no	—
204	D₄×C₁₉	—	4	1	no	—
205	D₄×C₁₉	—	4	4	no	—
206	D₄×C₁₉	—	4	4	no	—
207	D₄×C₁₉	—	4	2	no	—
208	D₄×C₁₉	—	4	4	no	—
209	D₄×C₁₉	—	4	2	no	—
210	D₄×C₁₉	—	4	1	no	—
211	D₄×C₁₉	—	4	2	no	—
212	D₄×C₁₉	—	4	2	no	—
213	D₄×C₁₉	—	8	1	no	—
214	D₄×C₁₉	—	8	4	no	—
215	D₄×C₁₉	—	8	4	no	—
216	D₄×C₁₉	—	8	2	no	—
217	D₄×C₁₉	—	8	4	no	—
218	D₄×C₁₉	—	8	2	no	—
219	C₂×C₄×C₁₉	—	2	1	no	—
220	C₂×C₄×C₁₉	—	2	1	no	—
221	C₂×C₄×C₁₉	—	2	2	no	—
222	C₂×C₄×C₁₉	—	2	2	no	—
223	C₂×C₄×C₁₉	—	2	1	no	—
224	C₂×C₄×C₁₉	—	2	1	no	—
225	C₂×C₄×C₁₉	—	2	1	no	—
226	C₂×C₄×C₁₉	—	2	4	no	—
227	C₂×C₄×C₁₉	—	4	8	no	—
228	C₂×C₄×C₁₉	—	4	2	no	—
229	C₂×C₄×C₁₉	—	4	4	no	—
230	C₂×C₄×C₁₉	—	4	2	no	—
231	C₂×C₄×C₁₉	—	4	1	no	—
232	C₂×C₄×C₁₉	—	4	2	no	—
233	C₂×C₄×C₁₉	—	4	1	no	—
234	C₂×C₄×C₁₉	—	4	1	no	—
235	C₂×C₄×C₁₉	—	4	2	no	—
236	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
237	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
239	C₈×C₁₉	—	4	4	no	—
240	C₈×C₁₉	—	4	2	no	—
241	#3549	C₂×C₁₉	1	1	yes	characteristic, complemented
242	#3021	C₂×C₁₉	1	2	yes	complemented
243	#3018	C₂×C₁₉	1	1	yes	characteristic, complemented
244	#2204	C₂×C₁₉	1	4	yes	complemented
245	#2202	C₂×C₁₉	1	4	yes	complemented
246	#2134	C₂×C₁₉	1	2	yes	complemented
247	#2132	C₂×C₁₉	1	1	yes	characteristic, complemented
248	C₂²×C₁₉	—	2	1	no	—
249	C₂²×C₁₉	—	2	2	no	—
250	C₂²×C₁₉	—	4	1	no	—
251	C₂²×C₁₉	—	4	2	no	—
252	C₂²×C₁₉	—	4	4	no	—
253	C₂²×C₁₉	—	4	4	no	—
254	C₂²×C₁₉	—	4	2	no	—
255	C₂²×C₁₉	—	4	2	no	—
256	C₂²×C₁₉	—	4	1	no	—
257	C₂²×C₁₉	—	4	4	no	—
258	C₂²×C₁₉	—	16	1	no	—
259	C₂²×C₁₉	—	16	2	no	—
260	C₂²×C₁₉	—	16	4	no	—
261	C₂²×C₁₉	—	16	4	no	—
262	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
263	C₄×C₁₉	—	2	2	no	—
264	C₄×C₁₉	—	2	2	no	—
265	C₄×C₁₉	—	2	1	no	—
266	C₄×C₁₉	—	4	4	no	—
267	C₄×C₁₉	—	4	1	no	—
268	C₄×C₁₉	—	4	1	no	—
269	C₄×C₁₉	—	4	2	no	—
270	C₄×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
271	C₄×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
272	#585	C₂²×C₁₉	1	1	yes	characteristic, complemented
273	#575	—	2	1	no	—
274	C₂×AGL(1,ℤ/8)	—	2	2	no	—
275	H(3,𝔽₄)	—	2	1	no	—
276	H(3,𝔽₄)	C₂²×C₁₉	1	2	yes	complemented
277	#555	—	2	2	no	—
278	#555	C₂²×C₁₉	1	2	yes	complemented
279	D₄²	—	2	2	no	—
280	D₄²	—	2	1	no	—
281	#535	—	2	1	no	—
282	#535	—	2	4	no	—
283	#535	C₂²×C₁₉	1	2	yes	—
284	#532	—	2	1	no	—
285	#532	C₂²×C₁₉	1	1	yes	characteristic
286	#456	C₂²×C₁₉	1	2	yes	complemented
287	#455	—	2	1	no	—
288	#454	C₂²×C₁₉	1	2	yes	complemented
289	#454	C₂²×C₁₉	1	8	yes	complemented
290	#453	—	2	1	no	—
291	#453	—	2	4	no	—
292	#421	—	2	2	no	—
293	C₂×#104	—	2	1	no	—
294	#413	C₂²×C₁₉	1	2	yes	complemented
295	#413	C₂²×C₁₉	1	1	yes	characteristic, complemented
296	#356	C₂²×C₁₉	1	2	yes	complemented
297	#355	C₂²×C₁₉	1	2	yes	complemented
298	#355	C₂²×C₁₉	1	8	yes	complemented
299	C₂×C₁₉	—	2	1	no	—
300	C₂×C₁₉	—	4	1	no	—
301	C₂×C₁₉	—	4	2	no	—
302	C₂×C₁₉	—	8	4	no	—
303	C₂×C₁₉	—	8	1	no	—
304	C₂×C₁₉	—	8	2	no	—
305	C₂×C₁₉	C₂×B(4,𝔽₂)	1	1	yes	characteristic
306	2₋¹⁺⁴	—	4	1	no	—
307	2₋¹⁺⁴	C₂³×C₁₉	1	2	yes	—
308	H(5,𝔽₂)	—	2	2	no	—
309	H(5,𝔽₂)	—	2	1	no	—
310	H(5,𝔽₂)	—	4	1	no	—
311	C₂×#41	—	2	2	no	—
312	C₂×#41	—	2	2	no	—
313	C₂×#41	—	2	1	no	—
314	C₂×#41	—	4	2	no	—
315	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
316	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
317	C₂²×D₄	—	2	4	no	—
318	C₂²×D₄	—	2	1	no	—
319	C₂²×D₄	D₄×C₁₉	1	2	yes	—
320	#137	—	2	2	no	—
321	#137	—	4	1	no	—
322	AGL(1,ℤ/8)	—	2	8	no	—
323	AGL(1,ℤ/8)	—	2	2	no	—
324	AGL(1,ℤ/8)	—	4	1	no	—
325	AGL(1,ℤ/8)	—	4	4	no	—
326	#135	—	4	2	no	—
327	C₂×SD₁₆	—	4	2	no	—
328	C₂×D₈	—	4	2	no	—
329	C₂×M₁₆	—	2	2	no	—
330	C₂×M₁₆	—	2	1	no	—
331	C₄⋊Q₈	—	2	1	no	—
332	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
333	#127	—	2	1	no	—
334	#127	—	2	2	no	—
335	#127	D₄×C₁₉	1	1	yes	characteristic
336	#127	D₄×C₁₉	1	4	yes	—
337	#124	—	2	4	no	—
338	#124	—	2	2	no	—
339	#124	—	2	2	no	—
340	#124	—	2	4	no	—
341	#124	D₄×C₁₉	1	1	yes	characteristic
342	#124	C₂³×C₁₉	1	1	yes	characteristic
343	#124	C₂³×C₁₉	1	4	yes	—
344	#121	—	2	2	no	—
345	#121	—	2	2	no	—
346	#121	—	2	4	no	—
347	#121	—	2	2	no	—
348	#121	—	2	4	no	—
349	#121	—	2	2	no	—
350	#121	—	2	2	no	—
351	#120	—	2	2	no	—
352	#120	—	2	4	no	—
353	#120	—	2	2	no	—
354	#120	—	2	2	no	—
355	#120	—	2	4	no	—
356	#120	—	2	2	no	—
357	C₄×D₄	—	2	2	no	—
358	C₄×D₄	—	2	2	no	—
359	C₄×D₄	—	2	2	no	—
360	#117	—	2	1	no	—
361	#117	—	2	4	no	—
362	#117	D₄×C₁₉	1	2	yes	—
363	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
364	#104	—	2	2	no	—
365	#104	—	2	2	no	—
366	#104	—	2	8	no	—
367	#101	C₂³×C₁₉	1	2	yes	—
368	#101	C₂³×C₁₉	1	4	yes	—
369	#100	—	2	2	no	—
370	#100	—	2	1	no	—
371	C₁₉	#33570	1	1	yes	characteristic, direct product factor, Sylow
372	C₂⁴	—	2	2	no	—
373	C₂⁴	—	2	2	no	—
374	#41	—	2	2	no	—
375	#41	—	2	4	no	—
376	#41	—	2	4	no	—
377	#41	—	2	2	no	—
378	#41	—	4	1	no	—
379	#41	—	4	1	no	—
380	#41	—	4	2	no	—
381	#41	—	4	1	no	—
382	#41	—	4	1	no	—
383	#41	—	4	1	no	—
384	#41	—	4	2	no	—
385	#41	—	4	4	no	—
386	#41	—	4	2	no	—
387	#41	—	4	1	no	—
388	#41	—	8	4	no	—
389	C₂×Q₈	—	2	2	no	—
390	C₂×Q₈	—	2	2	no	—
391	C₂×Q₈	—	2	1	no	—
392	C₂×Q₈	—	4	2	no	—
393	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
394	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
395	C₂×D₄	—	2	2	no	—
396	C₂×D₄	—	2	1	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	2	4	no	—
402	C₂×D₄	—	2	4	no	—
403	C₂×D₄	—	2	1	no	—
404	C₂×D₄	—	2	4	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	4	2	no	—
407	C₂×D₄	—	4	2	no	—
408	C₂×D₄	—	4	4	no	—
409	C₂×D₄	—	4	2	no	—
410	C₂×D₄	—	4	2	no	—
411	C₂×D₄	—	4	1	no	—
412	C₂×D₄	—	8	8	no	—
413	C₂×D₄	—	8	1	no	—
414	C₂×D₄	—	8	1	no	—
415	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
416	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
417	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
418	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
419	C₂²×C₄	—	2	4	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	4	1	no	—
423	C₂²×C₄	—	4	2	no	—
424	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
425	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
426	Q₁₆	—	4	2	no	—
427	SD₁₆	—	4	2	no	—
428	SD₁₆	—	4	8	no	—
429	SD₁₆	—	4	2	no	—
430	D₈	—	4	8	no	—
431	D₈	—	4	2	no	—
432	M₁₆	—	2	4	no	—
433	M₁₆	—	2	2	no	—
434	M₁₆	—	4	2	no	—
435	M₁₆	—	4	1	no	—
436	C₂×C₈	—	4	2	no	—
437	C₂×C₈	—	4	1	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	2	2	no	—
441	C₂²⋊C₄	—	2	4	no	—
442	C₂²⋊C₄	—	2	2	no	—
443	C₂²⋊C₄	—	2	4	no	—
444	C₂²⋊C₄	—	2	2	no	—
445	C₂²⋊C₄	—	2	2	no	—
446	C₂²⋊C₄	—	2	4	no	—
447	C₂²⋊C₄	—	2	2	no	—
448	C₂²⋊C₄	—	2	4	no	—
449	C₄²	—	2	2	no	—
450	C₄²	—	2	1	no	—
451	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
452	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
453	C₄²	C₂×D₄×C₁₉	1	4	yes	—
454	C₂³	—	2	4	no	—
455	C₂³	—	2	1	no	—
456	C₂³	—	4	1	no	—
457	C₂³	—	4	2	no	—
458	C₂³	—	8	2	no	—
459	C₂³	—	8	4	no	—
460	C₂³	—	8	4	no	—
461	C₂³	—	8	2	no	—
462	C₂³	C₁₉×#120	1	2	yes	—
463	C₂³	C₁₉×#120	1	1	yes	characteristic
464	Q₈	—	2	4	no	—
465	Q₈	—	2	2	no	—
466	Q₈	—	4	1	no	—
467	Q₈	—	4	1	no	—
468	Q₈	—	4	1	no	—
469	Q₈	—	8	2	no	—
470	D₄	—	2	4	no	—
471	D₄	—	2	2	no	—
472	D₄	—	4	2	no	—
473	D₄	—	4	1	no	—
474	D₄	—	4	4	no	—
475	D₄	—	4	1	no	—
476	D₄	—	4	4	no	—
477	D₄	—	4	4	no	—
478	D₄	—	4	2	no	—
479	D₄	—	4	4	no	—
480	D₄	—	4	2	no	—
481	D₄	—	4	1	no	—
482	D₄	—	4	2	no	—
483	D₄	—	4	2	no	—
484	D₄	—	8	1	no	—
485	D₄	—	8	4	no	—
486	D₄	—	8	4	no	—
487	D₄	—	8	2	no	—
488	D₄	—	8	4	no	—
489	D₄	—	8	2	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	4	8	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	4	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
508	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
509	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
510	C₈	—	4	4	no	—
511	C₈	—	4	2	no	—
512	C₂²	—	2	1	no	—
513	C₂²	—	2	2	no	—
514	C₂²	—	4	1	no	—
515	C₂²	—	4	2	no	—
516	C₂²	—	4	4	no	—
517	C₂²	—	4	4	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	4	1	no	—
521	C₂²	—	4	4	no	—
522	C₂²	—	16	2	no	—
523	C₂²	—	16	1	no	—
524	C₂²	—	16	4	no	—
525	C₂²	—	16	4	no	—
526	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
527	C₄	—	2	2	no	—
528	C₄	—	2	2	no	—
529	C₄	—	2	1	no	—
530	C₄	—	4	4	no	—
531	C₄	—	4	1	no	—
532	C₄	—	4	1	no	—
533	C₄	—	4	2	no	—
534	C₄	C₁₉×B(4,𝔽₂)	1	1	yes	characteristic
535	C₄	C₁₉×B(4,𝔽₂)	1	1	yes	characteristic
536	C₂	—	2	1	no	—
537	C₂	—	4	2	no	—
538	C₂	—	4	1	no	—
539	C₂	—	8	4	no	—
540	C₂	—	8	1	no	—
541	C₂	—	8	2	no	—
542	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 ◁ 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×#3549	C₂	semidirect
2. C₁₉×#3021	C₂	semidirect
3. C₁₉×#3018	C₂	semidirect
4. C₁₉×#2204	C₂	semidirect
5. C₁₉×#2202	C₂	semidirect
6. C₁₉×#2134	C₂	semidirect
7. C₁₉×#2132	C₂	semidirect
8. C₁₉×#585	C₂²	semidirect
12. C₁₉×H(3,𝔽₄)	C₂²	semidirect
14. C₁₉×#555	C₂²	semidirect
22. C₁₉×#456	C₂²	semidirect
24. C₁₉×#454	C₂²	semidirect
25. C₁₉×#454	C₂²	semidirect
30. C₁₉×#413	C₂²	semidirect
31. C₁₉×#413	C₂²	semidirect
32. C₁₉×#356	C₂²	semidirect
33. C₁₉×#355	C₂²	semidirect
34. C₁₉×#355	C₂²	semidirect
182. #33570	C₁₉	direct (N × H)
241. #3549	C₂×C₁₉	semidirect
242. #3021	C₂×C₁₉	semidirect
243. #3018	C₂×C₁₉	semidirect
244. #2204	C₂×C₁₉	semidirect
245. #2202	C₂×C₁₉	semidirect
246. #2134	C₂×C₁₉	semidirect
247. #2132	C₂×C₁₉	semidirect
272. #585	C₂²×C₁₉	semidirect
276. H(3,𝔽₄)	C₂²×C₁₉	semidirect
278. #555	C₂²×C₁₉	semidirect
286. #456	C₂²×C₁₉	semidirect
288. #454	C₂²×C₁₉	semidirect
289. #454	C₂²×C₁₉	semidirect
294. #413	C₂²×C₁₉	semidirect
295. #413	C₂²×C₁₉	semidirect
296. #356	C₂²×C₁₉	semidirect
297. #355	C₂²×C₁₉	semidirect
298. #355	C₂²×C₁₉	semidirect
371. C₁₉	#33570	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×#3549	2
C₁₉×#3021	2
C₁₉×#3018	2
C₁₉×#2204	2
C₁₉×#2202	2
C₁₉×#2134	2
C₁₉×#2132	2
#33570	19

Subgroups — C19×#33570 #18039529

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#33570 #18039529