Subgroups — C₁₉×#32699 #18038658

Order 4864.

538 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2102	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#2081	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2081	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2070	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2048	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#2003	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1967	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1932	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1915	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1912	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1903	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#1888	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1861	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1841	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1830	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
17	C₁₉×#568	C₂²	1	1	yes	characteristic
18	C₁₉×#536	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
20	C₁₉×#519	C₂²	1	1	yes	characteristic
21	C₁₉×#430	C₂²	1	1	yes	characteristic
22	C₁₉×#430	C₂²	1	1	yes	characteristic
23	C₁₉×#430	C₂²	1	1	yes	characteristic
24	C₁₉×#423	C₂²	1	1	yes	characteristic
25	C₁₉×#421	C₂²	1	1	yes	characteristic
26	C₁₉×#421	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
28	C₁₉×#418	C₂²	1	1	yes	characteristic
29	C₁₉×#418	C₂²	1	1	yes	characteristic
30	C₁₉×#418	C₂²	1	1	yes	characteristic
31	C₁₉×#413	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic
33	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic
34	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic
35	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic
36	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic
38	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
39	C₁₉×#344	C₂²	1	1	yes	characteristic
40	C₁₉×#344	C₂²	1	1	yes	characteristic
41	C₁₉×#344	C₂²	1	1	yes	characteristic
42	C₁₉×#344	C₂²	1	1	yes	characteristic
43	C₁₉×#344	C₂²	1	1	yes	characteristic
44	C₁₉×#344	C₂²	1	1	yes	characteristic
45	C₁₉×#339	C₂²	1	1	yes	characteristic
46	C₁₉×#339	C₂²	1	1	yes	characteristic
47	C₁₉×#339	C₂²	1	1	yes	characteristic
48	C₁₉×#338	C₂²	1	1	yes	characteristic
49	C₁₉×H(3,ℤ/4)	C₂²	1	1	yes	characteristic
50	C₁₉×H(3,ℤ/4)	C₂²	1	1	yes	characteristic
51	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
52	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
53	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
54	C₁₉×AGL(1,ℤ/8)	—	4	1	no	—
55	C₁₉×AGL(1,ℤ/8)	—	4	1	no	—
56	C₂×SD₁₆×C₁₉	—	2	1	no	—
57	C₂×D₈×C₁₉	—	2	1	no	—
58	C₁₉×#131	—	4	1	no	—
59	C₁₉×#131	—	4	1	no	—
60	C₂×M₁₆×C₁₉	—	4	1	no	—
61	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
62	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
63	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
64	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
65	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
66	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
67	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
68	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
69	C₁₉×C₄⋊Q₈	—	2	1	no	—
70	C₁₉×#124	—	2	1	no	—
71	C₁₉×#124	—	2	1	no	—
72	C₁₉×#124	—	2	1	no	—
73	C₁₉×#124	—	4	1	no	—
74	C₁₉×#123	—	2	2	no	—
75	C₁₉×C₂²⋊Q₈	—	4	1	no	—
76	C₄×Q₈×C₁₉	—	4	1	no	—
77	C₄×Q₈×C₁₉	—	4	1	no	—
78	C₁₉×#117	—	2	2	no	—
79	C₁₉×#117	C₂³	1	1	yes	characteristic
80	C₁₉×#117	C₂³	1	1	yes	characteristic
81	C₁₉×#117	C₂³	1	1	yes	characteristic
82	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
83	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
84	C₁₉×#108	—	4	1	no	—
85	C₁₉×#108	—	4	1	no	—
86	C₁₉×#108	—	4	1	no	—
87	C₁₉×C₄⋊C₈	—	4	1	no	—
88	C₁₉×#104	—	2	1	no	—
89	C₁₉×#104	—	2	1	no	—
90	C₁₉×#104	—	4	1	no	—
91	C₁₉×#104	—	4	1	no	—
92	C₁₉×#102	—	4	1	no	—
93	C₁₉×#102	—	4	1	no	—
94	C₁₉×#102	—	4	1	no	—
95	C₁₉×#101	—	2	1	no	—
96	C₁₉×#101	—	4	1	no	—
97	C₁₉×#101	—	4	1	no	—
98	C₁₉×#101	—	4	1	no	—
99	C₁₉×#101	—	4	1	no	—
100	C₁₉×#100	—	2	1	no	—
101	C₁₉×#100	—	4	1	no	—
102	C₁₉×#100	—	4	1	no	—
103	C₁₉×#97	—	2	1	no	—
104	C₄×C₈×C₁₉	—	2	1	no	—
105	C₂⁴×C₁₉	—	2	1	no	—
106	#41×C₁₉	—	2	1	no	—
107	#41×C₁₉	—	2	1	no	—
108	#41×C₁₉	—	2	1	no	—
109	#41×C₁₉	—	2	1	no	—
110	C₂×Q₈×C₁₉	—	2	1	no	—
111	C₂×Q₈×C₁₉	—	2	1	no	—
112	C₂×Q₈×C₁₉	—	2	1	no	—
113	C₂×Q₈×C₁₉	—	2	1	no	—
114	C₂×Q₈×C₁₉	—	2	1	no	—
115	C₂×Q₈×C₁₉	—	2	1	no	—
116	C₂×Q₈×C₁₉	#41	1	1	yes	characteristic
117	C₂×D₄×C₁₉	—	2	1	no	—
118	C₂×D₄×C₁₉	—	2	1	no	—
119	C₂×D₄×C₁₉	—	2	1	no	—
120	C₂×D₄×C₁₉	—	2	1	no	—
121	C₂×D₄×C₁₉	—	2	1	no	—
122	C₂×D₄×C₁₉	—	2	1	no	—
123	C₂×D₄×C₁₉	—	2	1	no	—
124	C₂×D₄×C₁₉	#41	1	1	yes	characteristic
125	C₂²×C₄×C₁₉	—	2	1	no	—
126	C₂²×C₄×C₁₉	—	2	1	no	—
127	C₂²×C₄×C₁₉	#41	1	2	yes	—
128	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
129	SD₁₆×C₁₉	—	4	2	no	—
130	D₈×C₁₉	—	4	2	no	—
131	M₁₆×C₁₉	—	2	1	no	—
132	M₁₆×C₁₉	—	2	1	no	—
133	M₁₆×C₁₉	—	2	1	no	—
134	M₁₆×C₁₉	—	2	1	no	—
135	M₁₆×C₁₉	—	2	1	no	—
136	M₁₆×C₁₉	—	2	1	no	—
137	M₁₆×C₁₉	—	2	1	no	—
138	M₁₆×C₁₉	—	2	1	no	—
139	M₁₆×C₁₉	—	2	1	no	—
140	M₁₆×C₁₉	—	2	1	no	—
141	M₁₆×C₁₉	—	2	1	no	—
142	M₁₆×C₁₉	—	2	1	no	—
143	M₁₆×C₁₉	—	2	1	no	—
144	M₁₆×C₁₉	—	2	1	no	—
145	M₁₆×C₁₉	—	2	1	no	—
146	M₁₆×C₁₉	—	2	1	no	—
147	M₁₆×C₁₉	—	4	2	no	—
148	C₂×C₈×C₁₉	—	2	1	no	—
149	C₂×C₈×C₁₉	—	2	1	no	—
150	C₂×C₈×C₁₉	—	2	1	no	—
151	C₂×C₈×C₁₉	—	2	1	no	—
152	C₂×C₈×C₁₉	—	2	1	no	—
153	C₂×C₈×C₁₉	—	2	1	no	—
154	C₂×C₈×C₁₉	—	2	1	no	—
155	C₂×C₈×C₁₉	—	2	1	no	—
156	C₂×C₈×C₁₉	—	4	2	no	—
157	C₄⋊C₄×C₁₉	—	2	1	no	—
158	C₄⋊C₄×C₁₉	—	2	1	no	—
159	C₄⋊C₄×C₁₉	—	2	1	no	—
160	C₄⋊C₄×C₁₉	—	4	2	no	—
161	C₄⋊C₄×C₁₉	—	4	2	no	—
162	C₂²⋊C₄×C₁₉	—	2	1	no	—
163	C₂²⋊C₄×C₁₉	—	2	1	no	—
164	C₂²⋊C₄×C₁₉	—	2	1	no	—
165	C₂²⋊C₄×C₁₉	—	4	2	no	—
166	C₂²⋊C₄×C₁₉	—	4	2	no	—
167	C₂²⋊C₄×C₁₉	—	4	2	no	—
168	C₄²×C₁₉	—	2	1	no	—
169	C₄²×C₁₉	—	2	1	no	—
170	C₄²×C₁₉	—	2	1	no	—
171	C₄²×C₁₉	—	2	1	no	—
172	C₄²×C₁₉	—	4	2	no	—
173	C₄²×C₁₉	#41	1	1	yes	characteristic
174	C₄²×C₁₉	#41	1	1	yes	characteristic
175	#32699	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
176	C₂³×C₁₉	—	2	1	no	—
177	C₂³×C₁₉	—	4	1	no	—
178	C₂³×C₁₉	—	4	1	no	—
179	C₂³×C₁₉	—	4	1	no	—
180	C₂³×C₁₉	—	8	2	no	—
181	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
182	Q₈×C₁₉	—	2	1	no	—
183	Q₈×C₁₉	—	2	1	no	—
184	Q₈×C₁₉	—	4	1	no	—
185	Q₈×C₁₉	—	4	1	no	—
186	Q₈×C₁₉	—	4	1	no	—
187	Q₈×C₁₉	—	4	1	no	—
188	D₄×C₁₉	—	2	1	no	—
189	D₄×C₁₉	—	2	1	no	—
190	D₄×C₁₉	—	4	1	no	—
191	D₄×C₁₉	—	4	1	no	—
192	D₄×C₁₉	—	4	1	no	—
193	D₄×C₁₉	—	4	1	no	—
194	D₄×C₁₉	—	4	1	no	—
195	D₄×C₁₉	—	4	1	no	—
196	C₂×C₄×C₁₉	—	2	2	no	—
197	C₂×C₄×C₁₉	—	2	1	no	—
198	C₂×C₄×C₁₉	—	2	1	no	—
199	C₂×C₄×C₁₉	—	2	2	no	—
200	C₂×C₄×C₁₉	—	2	2	no	—
201	C₂×C₄×C₁₉	—	2	1	no	—
202	C₂×C₄×C₁₉	—	4	1	no	—
203	C₂×C₄×C₁₉	—	4	1	no	—
204	C₂×C₄×C₁₉	—	4	1	no	—
205	C₂×C₄×C₁₉	—	4	1	no	—
206	C₂×C₄×C₁₉	—	4	1	no	—
207	C₂×C₄×C₁₉	—	8	1	no	—
208	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
209	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
210	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
211	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
212	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
213	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
214	C₈×C₁₉	—	4	1	no	—
215	C₈×C₁₉	—	4	1	no	—
216	C₈×C₁₉	—	4	1	no	—
217	C₈×C₁₉	—	4	1	no	—
218	C₈×C₁₉	—	4	1	no	—
219	C₈×C₁₉	—	4	1	no	—
220	C₈×C₁₉	—	4	1	no	—
221	C₈×C₁₉	—	4	1	no	—
222	#2102	C₂×C₁₉	1	1	yes	characteristic, complemented
223	#2081	C₂×C₁₉	1	1	yes	characteristic, complemented
224	#2081	C₂×C₁₉	1	1	yes	characteristic, complemented
225	#2070	C₂×C₁₉	1	1	yes	characteristic, complemented
226	#2048	C₂×C₁₉	1	1	yes	characteristic
227	#2003	C₂×C₁₉	1	1	yes	characteristic
228	#1967	C₂×C₁₉	1	1	yes	characteristic, complemented
229	#1932	C₂×C₁₉	1	1	yes	characteristic, complemented
230	#1915	C₂×C₁₉	1	1	yes	characteristic, complemented
231	#1912	C₂×C₁₉	1	1	yes	characteristic, complemented
232	#1903	C₂×C₁₉	1	1	yes	characteristic
233	#1888	C₂×C₁₉	1	1	yes	characteristic, complemented
234	#1861	C₂×C₁₉	1	1	yes	characteristic, complemented
235	#1841	C₂×C₁₉	1	1	yes	characteristic, complemented
236	#1830	C₂×C₁₉	1	1	yes	characteristic, complemented
237	C₂²×C₁₉	—	4	1	no	—
238	C₂²×C₁₉	—	4	1	no	—
239	C₂²×C₁₉	—	8	1	no	—
240	C₂²×C₁₉	—	8	2	no	—
241	C₂²×C₁₉	—	8	1	no	—
242	C₂²×C₁₉	—	16	1	no	—
243	C₂²×C₁₉	—	16	1	no	—
244	C₂²×C₁₉	#538	1	1	yes	characteristic
245	C₂²×C₁₉	#551	1	1	yes	characteristic
246	C₂²×C₁₉	#551	1	1	yes	characteristic
247	C₄×C₁₉	—	4	1	no	—
248	C₄×C₁₉	—	4	1	no	—
249	C₄×C₁₉	—	4	2	no	—
250	C₄×C₁₉	—	4	1	no	—
251	C₄×C₁₉	—	8	1	no	—
252	C₄×C₁₉	—	8	1	no	—
253	C₄×C₁₉	—	8	1	no	—
254	C₄×C₁₉	#538	1	1	yes	characteristic
255	C₄×C₁₉	#540	1	1	yes	characteristic
256	C₄×C₁₉	#553	1	1	yes	characteristic
257	C₄×C₁₉	#560	1	1	yes	characteristic
258	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	1	yes	characteristic
259	#568	C₂²×C₁₉	1	1	yes	characteristic
260	#536	C₂²×C₁₉	1	1	yes	characteristic
261	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
262	#519	C₂²×C₁₉	1	1	yes	characteristic
263	#430	C₂²×C₁₉	1	1	yes	characteristic
264	#430	C₂²×C₁₉	1	1	yes	characteristic
265	#430	C₂²×C₁₉	1	1	yes	characteristic
266	#423	C₂²×C₁₉	1	1	yes	characteristic
267	#421	C₂²×C₁₉	1	1	yes	characteristic
268	#421	C₂²×C₁₉	1	1	yes	characteristic
269	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
270	#418	C₂²×C₁₉	1	1	yes	characteristic
271	#418	C₂²×C₁₉	1	1	yes	characteristic
272	#418	C₂²×C₁₉	1	1	yes	characteristic
273	#413	C₂²×C₁₉	1	1	yes	characteristic
274	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic
275	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic
276	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic
277	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic
278	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
279	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
280	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
281	#344	C₂²×C₁₉	1	1	yes	characteristic
282	#344	C₂²×C₁₉	1	1	yes	characteristic
283	#344	C₂²×C₁₉	1	1	yes	characteristic
284	#344	C₂²×C₁₉	1	1	yes	characteristic
285	#344	C₂²×C₁₉	1	1	yes	characteristic
286	#344	C₂²×C₁₉	1	1	yes	characteristic
287	#339	C₂²×C₁₉	1	1	yes	characteristic
288	#339	C₂²×C₁₉	1	1	yes	characteristic
289	#339	C₂²×C₁₉	1	1	yes	characteristic
290	#338	C₂²×C₁₉	1	1	yes	characteristic
291	H(3,ℤ/4)	C₂²×C₁₉	1	1	yes	characteristic
292	H(3,ℤ/4)	C₂²×C₁₉	1	1	yes	characteristic
293	C₂×C₁₉	—	2	1	no	—
294	C₂×C₁₉	—	2	1	no	—
295	C₂×C₁₉	—	2	1	no	—
296	C₂×C₁₉	—	8	1	no	—
297	C₂×C₁₉	—	16	1	no	—
298	C₂×C₁₉	#2749	1	1	yes	characteristic
299	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
300	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
301	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
302	AGL(1,ℤ/8)	—	4	1	no	—
303	AGL(1,ℤ/8)	—	4	1	no	—
304	C₂×SD₁₆	—	2	1	no	—
305	C₂×D₈	—	2	1	no	—
306	#131	—	4	1	no	—
307	#131	—	4	1	no	—
308	C₂×M₁₆	—	4	1	no	—
309	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
310	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
311	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
312	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
313	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
314	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
315	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
316	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
317	C₄⋊Q₈	—	2	1	no	—
318	#124	—	2	1	no	—
319	#124	—	2	1	no	—
320	#124	—	2	1	no	—
321	#124	—	4	1	no	—
322	#123	—	2	2	no	—
323	C₂²⋊Q₈	—	4	1	no	—
324	C₄×Q₈	—	4	1	no	—
325	C₄×Q₈	—	4	1	no	—
326	#117	—	2	2	no	—
327	#117	C₂³×C₁₉	1	1	yes	characteristic
328	#117	C₂³×C₁₉	1	1	yes	characteristic
329	#117	C₂³×C₁₉	1	1	yes	characteristic
330	C₂×C₂²⋊C₄	—	2	2	no	—
331	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
332	#108	—	4	1	no	—
333	#108	—	4	1	no	—
334	#108	—	4	1	no	—
335	C₄⋊C₈	—	4	1	no	—
336	#104	—	2	1	no	—
337	#104	—	2	1	no	—
338	#104	—	4	1	no	—
339	#104	—	4	1	no	—
340	#102	—	4	1	no	—
341	#102	—	4	1	no	—
342	#102	—	4	1	no	—
343	#101	—	2	1	no	—
344	#101	—	4	1	no	—
345	#101	—	4	1	no	—
346	#101	—	4	1	no	—
347	#101	—	4	1	no	—
348	#100	—	2	1	no	—
349	#100	—	4	1	no	—
350	#100	—	4	1	no	—
351	#97	—	2	1	no	—
352	C₄×C₈	—	2	1	no	—
353	C₁₉	#32699	1	1	yes	characteristic, direct product factor, Sylow
354	C₂⁴	—	2	1	no	—
355	#41	—	2	1	no	—
356	#41	—	2	1	no	—
357	#41	—	2	1	no	—
358	#41	—	2	1	no	—
359	C₂×Q₈	—	2	1	no	—
360	C₂×Q₈	—	2	1	no	—
361	C₂×Q₈	—	2	1	no	—
362	C₂×Q₈	—	2	1	no	—
363	C₂×Q₈	—	2	1	no	—
364	C₂×Q₈	—	2	1	no	—
365	C₂×Q₈	#41×C₁₉	1	1	yes	characteristic
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	2	1	no	—
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	—	2	1	no	—
370	C₂×D₄	—	2	1	no	—
371	C₂×D₄	—	2	1	no	—
372	C₂×D₄	—	2	1	no	—
373	C₂×D₄	#41×C₁₉	1	1	yes	characteristic
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	#41×C₁₉	1	2	yes	—
377	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
378	SD₁₆	—	4	2	no	—
379	D₈	—	4	2	no	—
380	M₁₆	—	2	1	no	—
381	M₁₆	—	2	1	no	—
382	M₁₆	—	2	1	no	—
383	M₁₆	—	2	1	no	—
384	M₁₆	—	2	1	no	—
385	M₁₆	—	2	1	no	—
386	M₁₆	—	2	1	no	—
387	M₁₆	—	2	1	no	—
388	M₁₆	—	2	1	no	—
389	M₁₆	—	2	1	no	—
390	M₁₆	—	2	1	no	—
391	M₁₆	—	2	1	no	—
392	M₁₆	—	2	1	no	—
393	M₁₆	—	2	1	no	—
394	M₁₆	—	2	1	no	—
395	M₁₆	—	2	1	no	—
396	M₁₆	—	4	2	no	—
397	C₂×C₈	—	2	1	no	—
398	C₂×C₈	—	2	1	no	—
399	C₂×C₈	—	2	1	no	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	2	1	no	—
402	C₂×C₈	—	2	1	no	—
403	C₂×C₈	—	2	1	no	—
404	C₂×C₈	—	2	1	no	—
405	C₂×C₈	—	4	2	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	4	2	no	—
410	C₄⋊C₄	—	4	2	no	—
411	C₂²⋊C₄	—	2	1	no	—
412	C₂²⋊C₄	—	2	1	no	—
413	C₂²⋊C₄	—	2	1	no	—
414	C₂²⋊C₄	—	4	2	no	—
415	C₂²⋊C₄	—	4	2	no	—
416	C₂²⋊C₄	—	4	2	no	—
417	C₄²	—	2	1	no	—
418	C₄²	—	2	1	no	—
419	C₄²	—	2	1	no	—
420	C₄²	—	2	1	no	—
421	C₄²	—	4	2	no	—
422	C₄²	#41×C₁₉	1	1	yes	characteristic
423	C₄²	#41×C₁₉	1	1	yes	characteristic
424	C₂³	—	2	1	no	—
425	C₂³	—	4	1	no	—
426	C₂³	—	4	1	no	—
427	C₂³	—	4	1	no	—
428	C₂³	—	8	2	no	—
429	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
430	Q₈	—	2	1	no	—
431	Q₈	—	2	1	no	—
432	Q₈	—	4	1	no	—
433	Q₈	—	4	1	no	—
434	Q₈	—	4	1	no	—
435	Q₈	—	4	1	no	—
436	D₄	—	2	1	no	—
437	D₄	—	2	1	no	—
438	D₄	—	4	1	no	—
439	D₄	—	4	1	no	—
440	D₄	—	4	1	no	—
441	D₄	—	4	1	no	—
442	D₄	—	4	1	no	—
443	D₄	—	4	1	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	8	1	no	—
456	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
457	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
458	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
459	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
460	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
461	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
462	C₈	—	4	1	no	—
463	C₈	—	4	1	no	—
464	C₈	—	4	1	no	—
465	C₈	—	4	1	no	—
466	C₈	—	4	1	no	—
467	C₈	—	4	1	no	—
468	C₈	—	4	1	no	—
469	C₈	—	4	1	no	—
470	C₂²	—	4	1	no	—
471	C₂²	—	4	1	no	—
472	C₂²	—	8	1	no	—
473	C₂²	—	8	2	no	—
474	C₂²	—	8	1	no	—
475	C₂²	—	16	1	no	—
476	C₂²	—	16	1	no	—
477	C₂²	C₁₉×#538	1	1	yes	characteristic
478	C₂²	C₁₉×#551	1	1	yes	characteristic
479	C₂²	C₁₉×#551	1	1	yes	characteristic
480	C₄	—	4	1	no	—
481	C₄	—	4	1	no	—
482	C₄	—	4	2	no	—
483	C₄	—	4	1	no	—
484	C₄	—	8	1	no	—
485	C₄	—	8	1	no	—
486	C₄	—	8	1	no	—
487	C₄	C₁₉×#538	1	1	yes	characteristic
488	C₄	C₁₉×#540	1	1	yes	characteristic
489	C₄	C₁₉×#553	1	1	yes	characteristic
490	C₄	C₁₉×#560	1	1	yes	characteristic
491	C₂	—	2	1	no	—
492	C₂	—	2	1	no	—
493	C₂	—	2	1	no	—
494	C₂	—	8	1	no	—
495	C₂	—	16	1	no	—
496	C₂	C₁₉×#2749	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₉	#2749
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×AGL(1,ℤ/8)	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#2102	C₂	semidirect
2. C₁₉×#2081	C₂	semidirect
3. C₁₉×#2081	C₂	semidirect
4. C₁₉×#2070	C₂	semidirect
7. C₁₉×#1967	C₂	semidirect
8. C₁₉×#1932	C₂	semidirect
9. C₁₉×#1915	C₂	semidirect
10. C₁₉×#1912	C₂	semidirect
12. C₁₉×#1888	C₂	semidirect
13. C₁₉×#1861	C₂	semidirect
14. C₁₉×#1841	C₂	semidirect
15. C₁₉×#1830	C₂	semidirect
175. #32699	C₁₉	direct (N × H)
222. #2102	C₂×C₁₉	semidirect
223. #2081	C₂×C₁₉	semidirect
224. #2081	C₂×C₁₉	semidirect
225. #2070	C₂×C₁₉	semidirect
228. #1967	C₂×C₁₉	semidirect
229. #1932	C₂×C₁₉	semidirect
230. #1915	C₂×C₁₉	semidirect
231. #1912	C₂×C₁₉	semidirect
233. #1888	C₂×C₁₉	semidirect
234. #1861	C₂×C₁₉	semidirect
235. #1841	C₂×C₁₉	semidirect
236. #1830	C₂×C₁₉	semidirect
353. C₁₉	#32699	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×#2102	2
C₁₉×#2081	2
C₁₉×#2070	2
C₁₉×#2048	2
C₁₉×#2003	2
C₁₉×#1967	2
C₁₉×#1932	2
C₁₉×#1915	2
C₁₉×#1912	2
C₁₉×#1903	2
C₁₉×#1888	2
C₁₉×#1861	2
C₁₉×#1841	2
C₁₉×#1830	2
#32699	19

Subgroups — C19×#32699 #18038658

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32699 #18038658