Subgroups — C₁₉×#32698 #18038657

Order 4864.

594 conjugacy classes of subgroups.

The subgroup lattice has 518 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×#2069	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2048	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2002	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1965	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1932	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1914	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1911	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1903	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1887	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×#1829	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×#535	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
20	C₁₉×#518	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×#100	C₂²	1	1	yes	characteristic
33	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic
34	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic
35	C₂×C₁₉×#100	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×D₄×C₁₉	—	2	2	no	—
53	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
54	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
55	C₁₉×AGL(1,ℤ/8)	—	4	1	no	—
56	C₁₉×AGL(1,ℤ/8)	—	4	1	no	—
57	C₂×SD₁₆×C₁₉	—	2	1	no	—
58	C₂×D₈×C₁₉	—	2	1	no	—
59	C₁₉×#131	—	4	1	no	—
60	C₁₉×#131	—	4	1	no	—
61	C₂×M₁₆×C₁₉	—	4	1	no	—
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	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
70	C₁₉×#127	—	2	1	no	—
71	C₁₉×#127	—	2	1	no	—
72	C₁₉×#127	—	2	1	no	—
73	C₁₉×#127	—	4	1	no	—
74	C₁₉×#124	—	2	1	no	—
75	C₁₉×#121	—	4	1	no	—
76	C₁₉×#120	—	2	2	no	—
77	C₄×D₄×C₁₉	—	4	1	no	—
78	C₄×D₄×C₁₉	—	4	1	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×#100	—	2	1	no	—
97	C₁₉×#100	—	4	1	no	—
98	C₁₉×#100	—	4	1	no	—
99	C₁₉×#100	—	4	1	no	—
100	C₁₉×#100	—	4	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	C₂⁴×C₁₉	#41	1	2	yes	—
107	#41×C₁₉	—	2	1	no	—
108	#41×C₁₉	—	2	1	no	—
109	#41×C₁₉	—	2	1	no	—
110	#41×C₁₉	—	2	1	no	—
111	C₂×Q₈×C₁₉	#41	1	1	yes	characteristic
112	C₂×D₄×C₁₉	—	2	1	no	—
113	C₂×D₄×C₁₉	—	2	1	no	—
114	C₂×D₄×C₁₉	—	2	1	no	—
115	C₂×D₄×C₁₉	—	2	1	no	—
116	C₂×D₄×C₁₉	—	2	1	no	—
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	—	2	1	no	—
125	C₂×D₄×C₁₉	—	4	2	no	—
126	C₂×D₄×C₁₉	—	4	2	no	—
127	C₂×D₄×C₁₉	—	4	2	no	—
128	C₂×D₄×C₁₉	—	8	4	no	—
129	C₂×D₄×C₁₉	#41	1	1	yes	characteristic
130	C₂²×C₄×C₁₉	—	2	1	no	—
131	C₂²×C₄×C₁₉	—	2	1	no	—
132	C₂²×C₄×C₁₉	—	4	2	no	—
133	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
134	SD₁₆×C₁₉	—	4	2	no	—
135	D₈×C₁₉	—	4	2	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	—	2	1	no	—
148	M₁₆×C₁₉	—	2	1	no	—
149	M₁₆×C₁₉	—	2	1	no	—
150	M₁₆×C₁₉	—	2	1	no	—
151	M₁₆×C₁₉	—	2	1	no	—
152	M₁₆×C₁₉	—	4	2	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	—	2	1	no	—
157	C₂×C₈×C₁₉	—	2	1	no	—
158	C₂×C₈×C₁₉	—	2	1	no	—
159	C₂×C₈×C₁₉	—	2	1	no	—
160	C₂×C₈×C₁₉	—	2	1	no	—
161	C₂×C₈×C₁₉	—	4	2	no	—
162	C₄⋊C₄×C₁₉	—	2	1	no	—
163	C₄⋊C₄×C₁₉	—	2	1	no	—
164	C₄⋊C₄×C₁₉	—	2	1	no	—
165	C₂²⋊C₄×C₁₉	—	2	1	no	—
166	C₂²⋊C₄×C₁₉	—	2	1	no	—
167	C₂²⋊C₄×C₁₉	—	2	1	no	—
168	C₂²⋊C₄×C₁₉	—	4	2	no	—
169	C₂²⋊C₄×C₁₉	—	4	2	no	—
170	C₄²×C₁₉	—	2	1	no	—
171	C₄²×C₁₉	—	2	1	no	—
172	C₄²×C₁₉	—	2	1	no	—
173	C₄²×C₁₉	—	2	1	no	—
174	C₄²×C₁₉	#41	1	1	yes	characteristic
175	C₄²×C₁₉	#41	1	1	yes	characteristic
176	#32698	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
177	C₂³×C₁₉	—	2	2	no	—
178	C₂³×C₁₉	—	2	2	no	—
179	C₂³×C₁₉	—	2	1	no	—
180	C₂³×C₁₉	—	2	2	no	—
181	C₂³×C₁₉	—	4	1	no	—
182	C₂³×C₁₉	—	4	1	no	—
183	C₂³×C₁₉	—	4	1	no	—
184	C₂³×C₁₉	—	8	2	no	—
185	C₂³×C₁₉	—	8	2	no	—
186	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
187	Q₈×C₁₉	—	2	1	no	—
188	Q₈×C₁₉	—	2	1	no	—
189	D₄×C₁₉	—	2	1	no	—
190	D₄×C₁₉	—	2	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	D₄×C₁₉	—	4	1	no	—
197	D₄×C₁₉	—	4	1	no	—
198	D₄×C₁₉	—	4	1	no	—
199	D₄×C₁₉	—	4	1	no	—
200	D₄×C₁₉	—	4	1	no	—
201	D₄×C₁₉	—	8	4	no	—
202	D₄×C₁₉	—	8	4	no	—
203	D₄×C₁₉	—	16	2	no	—
204	C₂×C₄×C₁₉	—	2	1	no	—
205	C₂×C₄×C₁₉	—	2	1	no	—
206	C₂×C₄×C₁₉	—	2	1	no	—
207	C₂×C₄×C₁₉	—	4	2	no	—
208	C₂×C₄×C₁₉	—	4	1	no	—
209	C₂×C₄×C₁₉	—	4	1	no	—
210	C₂×C₄×C₁₉	—	4	1	no	—
211	C₂×C₄×C₁₉	—	4	1	no	—
212	C₂×C₄×C₁₉	—	4	1	no	—
213	C₂×C₄×C₁₉	—	16	2	no	—
214	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
215	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
216	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
217	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
218	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
219	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
220	C₈×C₁₉	—	4	1	no	—
221	C₈×C₁₉	—	4	1	no	—
222	C₈×C₁₉	—	4	1	no	—
223	C₈×C₁₉	—	4	1	no	—
224	C₈×C₁₉	—	4	1	no	—
225	C₈×C₁₉	—	4	1	no	—
226	C₈×C₁₉	—	4	1	no	—
227	C₈×C₁₉	—	4	1	no	—
228	#2102	C₂×C₁₉	1	1	yes	characteristic, complemented
229	#2081	C₂×C₁₉	1	1	yes	characteristic, complemented
230	#2081	C₂×C₁₉	1	1	yes	characteristic, complemented
231	#2069	C₂×C₁₉	1	1	yes	characteristic, complemented
232	#2048	C₂×C₁₉	1	1	yes	characteristic, complemented
233	#2002	C₂×C₁₉	1	1	yes	characteristic
234	#1965	C₂×C₁₉	1	1	yes	characteristic, complemented
235	#1932	C₂×C₁₉	1	1	yes	characteristic, complemented
236	#1914	C₂×C₁₉	1	1	yes	characteristic, complemented
237	#1911	C₂×C₁₉	1	1	yes	characteristic, complemented
238	#1903	C₂×C₁₉	1	1	yes	characteristic, complemented
239	#1887	C₂×C₁₉	1	1	yes	characteristic, complemented
240	#1861	C₂×C₁₉	1	1	yes	characteristic, complemented
241	#1841	C₂×C₁₉	1	1	yes	characteristic, complemented
242	#1829	C₂×C₁₉	1	1	yes	characteristic, complemented
243	C₂²×C₁₉	—	4	1	no	—
244	C₂²×C₁₉	—	4	1	no	—
245	C₂²×C₁₉	—	4	2	no	—
246	C₂²×C₁₉	—	8	2	no	—
247	C₂²×C₁₉	—	8	2	no	—
248	C₂²×C₁₉	—	8	1	no	—
249	C₂²×C₁₉	—	8	2	no	—
250	C₂²×C₁₉	—	8	2	no	—
251	C₂²×C₁₉	—	8	1	no	—
252	C₂²×C₁₉	—	16	1	no	—
253	C₂²×C₁₉	—	16	1	no	—
254	C₂²×C₁₉	#538	1	1	yes	characteristic
255	C₂²×C₁₉	#551	1	1	yes	characteristic
256	C₂²×C₁₉	#551	1	1	yes	characteristic
257	C₄×C₁₉	—	2	2	no	—
258	C₄×C₁₉	—	4	1	no	—
259	C₄×C₁₉	—	4	1	no	—
260	C₄×C₁₉	—	8	1	no	—
261	C₄×C₁₉	—	8	1	no	—
262	C₄×C₁₉	—	8	1	no	—
263	C₄×C₁₉	#538	1	1	yes	characteristic
264	C₄×C₁₉	#540	1	1	yes	characteristic
265	C₄×C₁₉	#553	1	1	yes	characteristic
266	C₄×C₁₉	#560	1	1	yes	characteristic
267	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	1	yes	characteristic
268	#568	C₂²×C₁₉	1	1	yes	characteristic
269	#535	C₂²×C₁₉	1	1	yes	characteristic
270	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
271	#518	C₂²×C₁₉	1	1	yes	characteristic
272	#430	C₂²×C₁₉	1	1	yes	characteristic
273	#430	C₂²×C₁₉	1	1	yes	characteristic
274	#430	C₂²×C₁₉	1	1	yes	characteristic
275	#423	C₂²×C₁₉	1	1	yes	characteristic
276	#421	C₂²×C₁₉	1	1	yes	characteristic
277	#421	C₂²×C₁₉	1	1	yes	characteristic
278	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
279	#418	C₂²×C₁₉	1	1	yes	characteristic
280	#418	C₂²×C₁₉	1	1	yes	characteristic
281	#418	C₂²×C₁₉	1	1	yes	characteristic
282	#413	C₂²×C₁₉	1	1	yes	characteristic
283	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
284	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
285	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
286	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
287	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
288	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
289	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
290	#344	C₂²×C₁₉	1	1	yes	characteristic
291	#344	C₂²×C₁₉	1	1	yes	characteristic
292	#344	C₂²×C₁₉	1	1	yes	characteristic
293	#344	C₂²×C₁₉	1	1	yes	characteristic
294	#344	C₂²×C₁₉	1	1	yes	characteristic
295	#344	C₂²×C₁₉	1	1	yes	characteristic
296	#339	C₂²×C₁₉	1	1	yes	characteristic
297	#339	C₂²×C₁₉	1	1	yes	characteristic
298	#339	C₂²×C₁₉	1	1	yes	characteristic
299	#338	C₂²×C₁₉	1	1	yes	characteristic
300	H(3,ℤ/4)	C₂²×C₁₉	1	1	yes	characteristic
301	H(3,ℤ/4)	C₂²×C₁₉	1	1	yes	characteristic
302	C₂×C₁₉	—	2	1	no	—
303	C₂×C₁₉	—	2	1	no	—
304	C₂×C₁₉	—	2	1	no	—
305	C₂×C₁₉	—	8	1	no	—
306	C₂×C₁₉	—	8	2	no	—
307	C₂×C₁₉	—	16	1	no	—
308	C₂×C₁₉	#2749	1	1	yes	characteristic
309	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
310	C₂²×D₄	—	2	2	no	—
311	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
312	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
313	AGL(1,ℤ/8)	—	4	1	no	—
314	AGL(1,ℤ/8)	—	4	1	no	—
315	C₂×SD₁₆	—	2	1	no	—
316	C₂×D₈	—	2	1	no	—
317	#131	—	4	1	no	—
318	#131	—	4	1	no	—
319	C₂×M₁₆	—	4	1	no	—
320	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
321	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
322	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
323	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
324	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
325	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
326	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
327	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
328	#127	—	2	1	no	—
329	#127	—	2	1	no	—
330	#127	—	2	1	no	—
331	#127	—	4	1	no	—
332	#124	—	2	1	no	—
333	#121	—	4	1	no	—
334	#120	—	2	2	no	—
335	C₄×D₄	—	4	1	no	—
336	C₄×D₄	—	4	1	no	—
337	#117	C₂³×C₁₉	1	1	yes	characteristic
338	#117	C₂³×C₁₉	1	1	yes	characteristic
339	#117	C₂³×C₁₉	1	1	yes	characteristic
340	C₂×C₂²⋊C₄	—	2	2	no	—
341	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
342	#108	—	4	1	no	—
343	#108	—	4	1	no	—
344	#108	—	4	1	no	—
345	C₄⋊C₈	—	4	1	no	—
346	#104	—	2	1	no	—
347	#104	—	2	1	no	—
348	#104	—	4	1	no	—
349	#104	—	4	1	no	—
350	#102	—	4	1	no	—
351	#102	—	4	1	no	—
352	#102	—	4	1	no	—
353	#101	—	2	1	no	—
354	#100	—	2	1	no	—
355	#100	—	4	1	no	—
356	#100	—	4	1	no	—
357	#100	—	4	1	no	—
358	#100	—	4	1	no	—
359	#100	—	4	1	no	—
360	#100	—	4	1	no	—
361	#97	—	2	1	no	—
362	C₄×C₈	—	2	1	no	—
363	C₁₉	#32698	1	1	yes	characteristic, direct product factor, Sylow
364	C₂⁴	—	2	1	no	—
365	C₂⁴	#41×C₁₉	1	2	yes	—
366	#41	—	2	1	no	—
367	#41	—	2	1	no	—
368	#41	—	2	1	no	—
369	#41	—	2	1	no	—
370	C₂×Q₈	#41×C₁₉	1	1	yes	characteristic
371	C₂×D₄	—	2	1	no	—
372	C₂×D₄	—	2	1	no	—
373	C₂×D₄	—	2	1	no	—
374	C₂×D₄	—	2	1	no	—
375	C₂×D₄	—	2	1	no	—
376	C₂×D₄	—	2	1	no	—
377	C₂×D₄	—	2	1	no	—
378	C₂×D₄	—	2	1	no	—
379	C₂×D₄	—	2	1	no	—
380	C₂×D₄	—	2	1	no	—
381	C₂×D₄	—	2	1	no	—
382	C₂×D₄	—	2	1	no	—
383	C₂×D₄	—	2	1	no	—
384	C₂×D₄	—	4	2	no	—
385	C₂×D₄	—	4	2	no	—
386	C₂×D₄	—	4	2	no	—
387	C₂×D₄	—	8	4	no	—
388	C₂×D₄	#41×C₁₉	1	1	yes	characteristic
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	4	2	no	—
392	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
393	SD₁₆	—	4	2	no	—
394	D₈	—	4	2	no	—
395	M₁₆	—	2	1	no	—
396	M₁₆	—	2	1	no	—
397	M₁₆	—	2	1	no	—
398	M₁₆	—	2	1	no	—
399	M₁₆	—	2	1	no	—
400	M₁₆	—	2	1	no	—
401	M₁₆	—	2	1	no	—
402	M₁₆	—	2	1	no	—
403	M₁₆	—	2	1	no	—
404	M₁₆	—	2	1	no	—
405	M₁₆	—	2	1	no	—
406	M₁₆	—	2	1	no	—
407	M₁₆	—	2	1	no	—
408	M₁₆	—	2	1	no	—
409	M₁₆	—	2	1	no	—
410	M₁₆	—	2	1	no	—
411	M₁₆	—	4	2	no	—
412	C₂×C₈	—	2	1	no	—
413	C₂×C₈	—	2	1	no	—
414	C₂×C₈	—	2	1	no	—
415	C₂×C₈	—	2	1	no	—
416	C₂×C₈	—	2	1	no	—
417	C₂×C₈	—	2	1	no	—
418	C₂×C₈	—	2	1	no	—
419	C₂×C₈	—	2	1	no	—
420	C₂×C₈	—	4	2	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	2	1	no	—
424	C₂²⋊C₄	—	2	1	no	—
425	C₂²⋊C₄	—	2	1	no	—
426	C₂²⋊C₄	—	2	1	no	—
427	C₂²⋊C₄	—	4	2	no	—
428	C₂²⋊C₄	—	4	2	no	—
429	C₄²	—	2	1	no	—
430	C₄²	—	2	1	no	—
431	C₄²	—	2	1	no	—
432	C₄²	—	2	1	no	—
433	C₄²	#41×C₁₉	1	1	yes	characteristic
434	C₄²	#41×C₁₉	1	1	yes	characteristic
435	C₂³	—	2	2	no	—
436	C₂³	—	2	2	no	—
437	C₂³	—	2	1	no	—
438	C₂³	—	2	2	no	—
439	C₂³	—	4	1	no	—
440	C₂³	—	4	1	no	—
441	C₂³	—	4	1	no	—
442	C₂³	—	8	2	no	—
443	C₂³	—	8	2	no	—
444	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
445	Q₈	—	2	1	no	—
446	Q₈	—	2	1	no	—
447	D₄	—	2	1	no	—
448	D₄	—	2	1	no	—
449	D₄	—	4	1	no	—
450	D₄	—	4	1	no	—
451	D₄	—	4	1	no	—
452	D₄	—	4	1	no	—
453	D₄	—	4	1	no	—
454	D₄	—	4	1	no	—
455	D₄	—	4	1	no	—
456	D₄	—	4	1	no	—
457	D₄	—	4	1	no	—
458	D₄	—	4	1	no	—
459	D₄	—	8	4	no	—
460	D₄	—	8	4	no	—
461	D₄	—	16	2	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	—	4	1	no	—
471	C₂×C₄	—	16	2	no	—
472	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
473	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
474	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
475	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
476	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
477	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
478	C₈	—	4	1	no	—
479	C₈	—	4	1	no	—
480	C₈	—	4	1	no	—
481	C₈	—	4	1	no	—
482	C₈	—	4	1	no	—
483	C₈	—	4	1	no	—
484	C₈	—	4	1	no	—
485	C₈	—	4	1	no	—
486	C₂²	—	4	1	no	—
487	C₂²	—	4	1	no	—
488	C₂²	—	4	2	no	—
489	C₂²	—	8	2	no	—
490	C₂²	—	8	2	no	—
491	C₂²	—	8	1	no	—
492	C₂²	—	8	2	no	—
493	C₂²	—	8	2	no	—
494	C₂²	—	8	1	no	—
495	C₂²	—	16	1	no	—
496	C₂²	—	16	1	no	—
497	C₂²	C₁₉×#538	1	1	yes	characteristic
498	C₂²	C₁₉×#551	1	1	yes	characteristic
499	C₂²	C₁₉×#551	1	1	yes	characteristic
500	C₄	—	2	2	no	—
501	C₄	—	4	1	no	—
502	C₄	—	4	1	no	—
503	C₄	—	8	1	no	—
504	C₄	—	8	1	no	—
505	C₄	—	8	1	no	—
506	C₄	C₁₉×#538	1	1	yes	characteristic
507	C₄	C₁₉×#540	1	1	yes	characteristic
508	C₄	C₁₉×#553	1	1	yes	characteristic
509	C₄	C₁₉×#560	1	1	yes	characteristic
510	C₂	—	2	1	no	—
511	C₂	—	2	1	no	—
512	C₂	—	2	1	no	—
513	C₂	—	8	2	no	—
514	C₂	—	8	1	no	—
515	C₂	—	16	1	no	—
516	C₂	C₁₉×#2749	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₉	#2749
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#2002	C₂
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×#2069	C₂	semidirect
5. C₁₉×#2048	C₂	semidirect
7. C₁₉×#1965	C₂	semidirect
8. C₁₉×#1932	C₂	semidirect
9. C₁₉×#1914	C₂	semidirect
10. C₁₉×#1911	C₂	semidirect
11. C₁₉×#1903	C₂	semidirect
12. C₁₉×#1887	C₂	semidirect
13. C₁₉×#1861	C₂	semidirect
14. C₁₉×#1841	C₂	semidirect
15. C₁₉×#1829	C₂	semidirect
176. #32698	C₁₉	direct (N × H)
228. #2102	C₂×C₁₉	semidirect
229. #2081	C₂×C₁₉	semidirect
230. #2081	C₂×C₁₉	semidirect
231. #2069	C₂×C₁₉	semidirect
232. #2048	C₂×C₁₉	semidirect
234. #1965	C₂×C₁₉	semidirect
235. #1932	C₂×C₁₉	semidirect
236. #1914	C₂×C₁₉	semidirect
237. #1911	C₂×C₁₉	semidirect
238. #1903	C₂×C₁₉	semidirect
239. #1887	C₂×C₁₉	semidirect
240. #1861	C₂×C₁₉	semidirect
241. #1841	C₂×C₁₉	semidirect
242. #1829	C₂×C₁₉	semidirect
363. C₁₉	#32698	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×#2069	2
C₁₉×#2048	2
C₁₉×#2002	2
C₁₉×#1965	2
C₁₉×#1932	2
C₁₉×#1914	2
C₁₉×#1911	2
C₁₉×#1903	2
C₁₉×#1887	2
C₁₉×#1861	2
C₁₉×#1841	2
C₁₉×#1829	2
#32698	19

Subgroups — C19×#32698 #18038657

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32698 #18038657