Subgroups — C₁₉×#32896 #18038855

Order 4864.

3610 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×H(7,𝔽₂)	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3028	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3022	C₂	1	3	yes	maximal, complemented
4	C₁₉×#3009	C₂	1	3	yes	maximal, complemented
5	C₁₉×#1795	C₂	1	3	yes	maximal, complemented
6	C₁₉×#1794	C₂	1	3	yes	maximal, complemented
7	C₁₉×#1791	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#585	—	2	6	no	—
9	C₁₉×#585	—	2	6	no	—
10	C₁₉×#585	C₂²	1	3	yes	—
11	C₁₉×#585	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×H(5,𝔽₂)	—	2	6	no	—
13	C₂×C₁₉×H(5,𝔽₂)	—	2	4	no	—
14	C₂×C₁₉×H(5,𝔽₂)	—	2	6	no	—
15	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	3	yes	—
16	C₂×C₁₉×#137	C₂²	1	3	yes	complemented
17	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
18	C₁₉×#536	C₂²	1	3	yes	complemented
19	C₁₉×#458	—	2	4	no	—
20	C₁₉×#456	—	2	6	no	—
21	C₁₉×#455	—	2	6	no	—
22	C₁₉×#452	—	2	6	no	—
23	C₁₉×#450	—	2	6	no	—
24	C₁₉×#421	C₂²	1	6	yes	complemented
25	C₁₉×#418	C₂²	1	3	yes	complemented
26	C₁₉×#416	C₂²	1	3	yes	complemented
27	C₁₉×#413	C₂²	1	3	yes	complemented
28	C₁₉×#410	C₂²	1	3	yes	complemented
29	C₁₉×#408	C₂²	1	3	yes	complemented
30	C₁₉×2₋¹⁺⁴	—	2	4	no	—
31	C₁₉×2₋¹⁺⁴	—	2	12	no	—
32	C₁₉×2₋¹⁺⁴	—	2	3	no	—
33	C₁₉×2₋¹⁺⁴	—	2	6	no	—
34	C₁₉×2₋¹⁺⁴	D₄	1	6	yes	—
35	C₁₉×H(5,𝔽₂)	—	2	12	no	—
36	C₁₉×H(5,𝔽₂)	—	2	24	no	—
37	C₁₉×H(5,𝔽₂)	—	2	24	no	—
38	C₁₉×H(5,𝔽₂)	—	2	12	no	—
39	C₁₉×H(5,𝔽₂)	—	2	24	no	—
40	C₁₉×H(5,𝔽₂)	—	2	12	no	—
41	C₁₉×H(5,𝔽₂)	—	2	6	no	—
42	C₁₉×H(5,𝔽₂)	—	2	3	no	—
43	C₁₉×H(5,𝔽₂)	—	2	6	no	—
44	C₁₉×H(5,𝔽₂)	—	2	12	no	—
45	C₁₉×H(5,𝔽₂)	D₄	1	6	yes	—
46	C₁₉×H(5,𝔽₂)	D₄	1	4	yes	—
47	C₂×#41×C₁₉	—	2	24	no	—
48	C₂×#41×C₁₉	—	2	12	no	—
49	C₂×#41×C₁₉	—	2	12	no	—
50	C₂×#41×C₁₉	—	2	24	no	—
51	C₂×#41×C₁₉	—	2	12	no	—
52	C₂×#41×C₁₉	—	2	3	no	—
53	C₂×#41×C₁₉	—	2	6	no	—
54	C₂×#41×C₁₉	—	2	6	no	—
55	C₂×#41×C₁₉	D₄	1	6	yes	—
56	C₂×#41×C₁₉	C₂³	1	3	yes	—
57	C₂×#41×C₁₉	C₂³	1	3	yes	—
58	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic, complemented
59	C₂²×D₄×C₁₉	—	2	24	no	—
60	C₂²×D₄×C₁₉	—	2	12	no	—
61	C₂²×D₄×C₁₉	—	2	4	no	—
62	C₂²×D₄×C₁₉	—	2	6	no	—
63	C₂²×D₄×C₁₉	—	2	3	no	—
64	C₂²×D₄×C₁₉	D₄	1	6	yes	—
65	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
66	C₁₉×#137	—	2	12	no	—
67	C₂×Q₁₆×C₁₉	—	2	3	no	—
68	C₂×SD₁₆×C₁₉	—	2	3	no	—
69	C₂×SD₁₆×C₁₉	—	2	6	no	—
70	C₂×M₁₆×C₁₉	C₂³	1	3	yes	complemented
71	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic, complemented
72	C₁₉×C₄⋊Q₈	—	2	3	no	—
73	C₁₉×#124	—	2	3	no	—
74	C₁₉×#123	—	2	6	no	—
75	C₁₉×C₂²⋊Q₈	—	2	6	no	—
76	C₁₉×#117	C₂³	1	3	yes	complemented
77	C₁₉×#104	—	2	12	no	—
78	C₁₉×#103	—	2	3	no	—
79	C₁₉×#102	—	2	3	no	—
80	C₁₉×#102	—	2	6	no	—
81	C₁₉×#101	—	2	3	no	—
82	C₁₉×#100	—	2	3	no	—
83	C₁₉×#99	—	2	6	no	—
84	C₁₉×C₂²⋊C₈	—	2	6	no	—
85	C₂⁴×C₁₉	—	2	8	no	—
86	C₂⁴×C₁₉	—	2	6	no	—
87	C₂⁴×C₁₉	—	2	1	no	—
88	#41×C₁₉	—	2	24	no	—
89	#41×C₁₉	—	2	24	no	—
90	#41×C₁₉	—	2	48	no	—
91	#41×C₁₉	—	2	24	no	—
92	#41×C₁₉	—	2	24	no	—
93	#41×C₁₉	—	2	12	no	—
94	#41×C₁₉	—	2	12	no	—
95	#41×C₁₉	—	2	12	no	—
96	#41×C₁₉	—	2	4	no	—
97	#41×C₁₉	—	2	12	no	—
98	#41×C₁₉	—	2	12	no	—
99	#41×C₁₉	—	2	12	no	—
100	#41×C₁₉	—	2	12	no	—
101	#41×C₁₉	—	2	12	no	—
102	#41×C₁₉	—	2	12	no	—
103	#41×C₁₉	—	2	6	no	—
104	#41×C₁₉	—	2	6	no	—
105	#41×C₁₉	—	2	6	no	—
106	#41×C₁₉	C₂×D₄	1	12	yes	—
107	C₂×Q₈×C₁₉	—	2	8	no	—
108	C₂×Q₈×C₁₉	—	2	6	no	—
109	C₂×Q₈×C₁₉	—	2	6	no	—
110	C₂×Q₈×C₁₉	—	2	12	no	—
111	C₂×Q₈×C₁₉	—	2	3	no	—
112	C₂×Q₈×C₁₉	—	2	3	no	—
113	C₂×Q₈×C₁₉	C₂×D₄	1	3	yes	—
114	C₂×Q₈×C₁₉	C₂×D₄	1	3	yes	—
115	C₂×D₄×C₁₉	—	2	24	no	—
116	C₂×D₄×C₁₉	—	2	48	no	—
117	C₂×D₄×C₁₉	—	2	24	no	—
118	C₂×D₄×C₁₉	—	2	24	no	—
119	C₂×D₄×C₁₉	—	2	24	no	—
120	C₂×D₄×C₁₉	—	2	48	no	—
121	C₂×D₄×C₁₉	—	2	24	no	—
122	C₂×D₄×C₁₉	—	2	6	no	—
123	C₂×D₄×C₁₉	—	2	6	no	—
124	C₂×D₄×C₁₉	—	2	12	no	—
125	C₂×D₄×C₁₉	—	2	12	no	—
126	C₂×D₄×C₁₉	—	2	6	no	—
127	C₂×D₄×C₁₉	—	2	3	no	—
128	C₂×D₄×C₁₉	—	2	12	no	—
129	C₂×D₄×C₁₉	—	2	12	no	—
130	C₂×D₄×C₁₉	—	2	12	no	—
131	C₂×D₄×C₁₉	—	2	6	no	—
132	C₂×D₄×C₁₉	—	2	3	no	—
133	C₂×D₄×C₁₉	C₂×D₄	1	6	yes	—
134	C₂×D₄×C₁₉	C₂×D₄	1	3	yes	—
135	C₂×D₄×C₁₉	C₂×D₄	1	3	yes	—
136	C₂×D₄×C₁₉	C₂×D₄	1	6	yes	—
137	C₂²×C₄×C₁₉	—	2	24	no	—
138	C₂²×C₄×C₁₉	—	2	12	no	—
139	C₂²×C₄×C₁₉	—	2	4	no	—
140	C₂²×C₄×C₁₉	—	2	6	no	—
141	C₂²×C₄×C₁₉	—	2	3	no	—
142	C₂²×C₄×C₁₉	—	2	1	no	—
143	C₂²×C₄×C₁₉	C₂×D₄	1	6	yes	—
144	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
145	Q₁₆×C₁₉	—	4	6	no	—
146	SD₁₆×C₁₉	—	4	4	no	—
147	SD₁₆×C₁₉	—	4	6	no	—
148	M₁₆×C₁₉	—	2	6	no	—
149	C₂×C₈×C₁₉	—	2	3	no	—
150	C₂×C₈×C₁₉	—	2	3	no	—
151	C₄⋊C₄×C₁₉	—	2	3	no	—
152	C₄⋊C₄×C₁₉	—	4	6	no	—
153	C₂²⋊C₄×C₁₉	—	2	3	no	—
154	C₂²⋊C₄×C₁₉	—	4	6	no	—
155	C₄²×C₁₉	—	2	3	no	—
156	#32896	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
157	C₂³×C₁₉	—	2	4	no	—
158	C₂³×C₁₉	—	2	24	no	—
159	C₂³×C₁₉	—	2	12	no	—
160	C₂³×C₁₉	—	2	6	no	—
161	C₂³×C₁₉	—	2	3	no	—
162	C₂³×C₁₉	—	16	1	no	—
163	C₂³×C₁₉	—	16	6	no	—
164	C₂³×C₁₉	—	16	8	no	—
165	C₂³×C₁₉	#120	1	6	yes	—
166	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
167	Q₈×C₁₉	—	2	12	no	—
168	Q₈×C₁₉	—	2	4	no	—
169	Q₈×C₁₉	—	2	3	no	—
170	Q₈×C₁₉	—	2	6	no	—
171	Q₈×C₁₉	—	4	1	no	—
172	Q₈×C₁₉	—	4	3	no	—
173	Q₈×C₁₉	#120	1	6	yes	—
174	D₄×C₁₉	—	2	24	no	—
175	D₄×C₁₉	—	2	24	no	—
176	D₄×C₁₉	—	2	12	no	—
177	D₄×C₁₉	—	2	12	no	—
178	D₄×C₁₉	—	2	24	no	—
179	D₄×C₁₉	—	2	12	no	—
180	D₄×C₁₉	—	2	12	no	—
181	D₄×C₁₉	—	2	6	no	—
182	D₄×C₁₉	—	2	6	no	—
183	D₄×C₁₉	—	2	3	no	—
184	D₄×C₁₉	#120	1	6	yes	—
185	D₄×C₁₉	#120	1	4	yes	—
186	C₂×C₄×C₁₉	—	2	12	no	—
187	C₂×C₄×C₁₉	—	2	24	no	—
188	C₂×C₄×C₁₉	—	2	24	no	—
189	C₂×C₄×C₁₉	—	2	12	no	—
190	C₂×C₄×C₁₉	—	2	3	no	—
191	C₂×C₄×C₁₉	—	2	12	no	—
192	C₂×C₄×C₁₉	—	2	6	no	—
193	C₂×C₄×C₁₉	—	2	6	no	—
194	C₂×C₄×C₁₉	—	4	3	no	—
195	C₂×C₄×C₁₉	—	4	3	no	—
196	C₂×C₄×C₁₉	#120	1	6	yes	—
197	C₂×C₄×C₁₉	C₂²×D₄	1	3	yes	—
198	C₂×C₄×C₁₉	C₂²×D₄	1	3	yes	—
199	C₈×C₁₉	—	4	1	no	—
200	C₈×C₁₉	—	4	3	no	—
201	H(7,𝔽₂)	C₂×C₁₉	1	1	yes	characteristic
202	#3028	C₂×C₁₉	1	1	yes	characteristic, complemented
203	#3022	C₂×C₁₉	1	3	yes	complemented
204	#3009	C₂×C₁₉	1	3	yes	complemented
205	#1795	C₂×C₁₉	1	3	yes	complemented
206	#1794	C₂×C₁₉	1	3	yes	complemented
207	#1791	C₂×C₁₉	1	1	yes	characteristic, complemented
208	C₂²×C₁₉	—	2	6	no	—
209	C₂²×C₁₉	—	2	4	no	—
210	C₂²×C₁₉	—	2	6	no	—
211	C₂²×C₁₉	—	4	1	no	—
212	C₂²×C₁₉	—	4	6	no	—
213	C₂²×C₁₉	—	8	6	no	—
214	C₂²×C₁₉	—	8	3	no	—
215	C₂²×C₁₉	—	8	4	no	—
216	C₂²×C₁₉	—	8	24	no	—
217	C₂²×C₁₉	—	8	12	no	—
218	C₂²×C₁₉	C₂×#120	1	3	yes	—
219	C₄×C₁₉	—	2	6	no	—
220	C₄×C₁₉	—	2	6	no	—
221	C₄×C₁₉	—	8	3	no	—
222	C₄×C₁₉	—	8	1	no	—
223	C₄×C₁₉	C₂×#120	1	3	yes	—
224	C₄×C₁₉	C₂×#120	1	1	yes	characteristic
225	#585	—	2	6	no	—
226	#585	—	2	6	no	—
227	#585	C₂²×C₁₉	1	3	yes	—
228	#585	C₂²×C₁₉	1	1	yes	characteristic
229	C₂×H(5,𝔽₂)	—	2	6	no	—
230	C₂×H(5,𝔽₂)	—	2	4	no	—
231	C₂×H(5,𝔽₂)	—	2	6	no	—
232	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	3	yes	—
233	C₂×#137	C₂²×C₁₉	1	3	yes	complemented
234	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
235	#536	C₂²×C₁₉	1	3	yes	complemented
236	#458	—	2	4	no	—
237	#456	—	2	6	no	—
238	#455	—	2	6	no	—
239	#452	—	2	6	no	—
240	#450	—	2	6	no	—
241	#421	C₂²×C₁₉	1	6	yes	complemented
242	#418	C₂²×C₁₉	1	3	yes	complemented
243	#416	C₂²×C₁₉	1	3	yes	complemented
244	#413	C₂²×C₁₉	1	3	yes	complemented
245	#410	C₂²×C₁₉	1	3	yes	complemented
246	#408	C₂²×C₁₉	1	3	yes	complemented
247	C₂×C₁₉	—	2	3	no	—
248	C₂×C₁₉	—	4	6	no	—
249	C₂×C₁₉	—	4	4	no	—
250	C₂×C₁₉	—	4	6	no	—
251	C₂×C₁₉	#2846	1	1	yes	characteristic
252	2₋¹⁺⁴	—	2	4	no	—
253	2₋¹⁺⁴	—	2	12	no	—
254	2₋¹⁺⁴	—	2	3	no	—
255	2₋¹⁺⁴	—	2	6	no	—
256	2₋¹⁺⁴	D₄×C₁₉	1	6	yes	—
257	H(5,𝔽₂)	—	2	12	no	—
258	H(5,𝔽₂)	—	2	24	no	—
259	H(5,𝔽₂)	—	2	24	no	—
260	H(5,𝔽₂)	—	2	12	no	—
261	H(5,𝔽₂)	—	2	24	no	—
262	H(5,𝔽₂)	—	2	12	no	—
263	H(5,𝔽₂)	—	2	6	no	—
264	H(5,𝔽₂)	—	2	3	no	—
265	H(5,𝔽₂)	—	2	6	no	—
266	H(5,𝔽₂)	—	2	12	no	—
267	H(5,𝔽₂)	D₄×C₁₉	1	6	yes	—
268	H(5,𝔽₂)	D₄×C₁₉	1	4	yes	—
269	C₂×#41	—	2	24	no	—
270	C₂×#41	—	2	12	no	—
271	C₂×#41	—	2	12	no	—
272	C₂×#41	—	2	24	no	—
273	C₂×#41	—	2	12	no	—
274	C₂×#41	—	2	3	no	—
275	C₂×#41	—	2	6	no	—
276	C₂×#41	—	2	6	no	—
277	C₂×#41	D₄×C₁₉	1	6	yes	—
278	C₂×#41	C₂³×C₁₉	1	3	yes	—
279	C₂×#41	C₂³×C₁₉	1	3	yes	—
280	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic, complemented
281	C₂²×D₄	—	2	24	no	—
282	C₂²×D₄	—	2	12	no	—
283	C₂²×D₄	—	2	4	no	—
284	C₂²×D₄	—	2	6	no	—
285	C₂²×D₄	—	2	3	no	—
286	C₂²×D₄	D₄×C₁₉	1	6	yes	—
287	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
288	#137	—	2	12	no	—
289	C₂×Q₁₆	—	2	3	no	—
290	C₂×SD₁₆	—	2	6	no	—
291	C₂×SD₁₆	—	2	3	no	—
292	C₂×M₁₆	C₂³×C₁₉	1	3	yes	complemented
293	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic, complemented
294	C₄⋊Q₈	—	2	3	no	—
295	#124	—	2	3	no	—
296	#123	—	2	6	no	—
297	C₂²⋊Q₈	—	2	6	no	—
298	#117	C₂³×C₁₉	1	3	yes	complemented
299	#104	—	2	12	no	—
300	#103	—	2	3	no	—
301	#102	—	2	3	no	—
302	#102	—	2	6	no	—
303	#101	—	2	3	no	—
304	#100	—	2	3	no	—
305	#99	—	2	6	no	—
306	C₂²⋊C₈	—	2	6	no	—
307	C₁₉	#32896	1	1	yes	characteristic, direct product factor, Sylow
308	C₂⁴	—	2	8	no	—
309	C₂⁴	—	2	6	no	—
310	C₂⁴	—	2	1	no	—
311	#41	—	2	24	no	—
312	#41	—	2	24	no	—
313	#41	—	2	48	no	—
314	#41	—	2	24	no	—
315	#41	—	2	24	no	—
316	#41	—	2	12	no	—
317	#41	—	2	12	no	—
318	#41	—	2	12	no	—
319	#41	—	2	4	no	—
320	#41	—	2	12	no	—
321	#41	—	2	12	no	—
322	#41	—	2	12	no	—
323	#41	—	2	12	no	—
324	#41	—	2	12	no	—
325	#41	—	2	12	no	—
326	#41	—	2	6	no	—
327	#41	—	2	6	no	—
328	#41	—	2	6	no	—
329	#41	C₂×D₄×C₁₉	1	12	yes	—
330	C₂×Q₈	—	2	8	no	—
331	C₂×Q₈	—	2	6	no	—
332	C₂×Q₈	—	2	6	no	—
333	C₂×Q₈	—	2	12	no	—
334	C₂×Q₈	—	2	3	no	—
335	C₂×Q₈	—	2	3	no	—
336	C₂×Q₈	C₂×D₄×C₁₉	1	3	yes	—
337	C₂×Q₈	C₂×D₄×C₁₉	1	3	yes	—
338	C₂×D₄	—	2	24	no	—
339	C₂×D₄	—	2	48	no	—
340	C₂×D₄	—	2	24	no	—
341	C₂×D₄	—	2	24	no	—
342	C₂×D₄	—	2	24	no	—
343	C₂×D₄	—	2	48	no	—
344	C₂×D₄	—	2	24	no	—
345	C₂×D₄	—	2	6	no	—
346	C₂×D₄	—	2	6	no	—
347	C₂×D₄	—	2	12	no	—
348	C₂×D₄	—	2	12	no	—
349	C₂×D₄	—	2	6	no	—
350	C₂×D₄	—	2	3	no	—
351	C₂×D₄	—	2	12	no	—
352	C₂×D₄	—	2	12	no	—
353	C₂×D₄	—	2	12	no	—
354	C₂×D₄	—	2	6	no	—
355	C₂×D₄	—	2	3	no	—
356	C₂×D₄	C₂×D₄×C₁₉	1	6	yes	—
357	C₂×D₄	C₂×D₄×C₁₉	1	3	yes	—
358	C₂×D₄	C₂×D₄×C₁₉	1	3	yes	—
359	C₂×D₄	C₂×D₄×C₁₉	1	6	yes	—
360	C₂²×C₄	—	2	24	no	—
361	C₂²×C₄	—	2	12	no	—
362	C₂²×C₄	—	2	4	no	—
363	C₂²×C₄	—	2	6	no	—
364	C₂²×C₄	—	2	3	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	C₂×D₄×C₁₉	1	6	yes	—
367	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
368	Q₁₆	—	4	6	no	—
369	SD₁₆	—	4	4	no	—
370	SD₁₆	—	4	6	no	—
371	M₁₆	—	2	6	no	—
372	C₂×C₈	—	2	3	no	—
373	C₂×C₈	—	2	3	no	—
374	C₄⋊C₄	—	2	3	no	—
375	C₄⋊C₄	—	4	6	no	—
376	C₂²⋊C₄	—	2	3	no	—
377	C₂²⋊C₄	—	4	6	no	—
378	C₄²	—	2	3	no	—
379	C₂³	—	2	4	no	—
380	C₂³	—	2	24	no	—
381	C₂³	—	2	12	no	—
382	C₂³	—	2	6	no	—
383	C₂³	—	2	3	no	—
384	C₂³	—	16	1	no	—
385	C₂³	—	16	6	no	—
386	C₂³	—	16	8	no	—
387	C₂³	C₁₉×#120	1	6	yes	—
388	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
389	Q₈	—	2	12	no	—
390	Q₈	—	2	4	no	—
391	Q₈	—	2	3	no	—
392	Q₈	—	2	6	no	—
393	Q₈	—	4	1	no	—
394	Q₈	—	4	3	no	—
395	Q₈	C₁₉×#120	1	6	yes	—
396	D₄	—	2	24	no	—
397	D₄	—	2	24	no	—
398	D₄	—	2	12	no	—
399	D₄	—	2	12	no	—
400	D₄	—	2	24	no	—
401	D₄	—	2	12	no	—
402	D₄	—	2	12	no	—
403	D₄	—	2	6	no	—
404	D₄	—	2	6	no	—
405	D₄	—	2	3	no	—
406	D₄	C₁₉×#120	1	6	yes	—
407	D₄	C₁₉×#120	1	4	yes	—
408	C₂×C₄	—	2	12	no	—
409	C₂×C₄	—	2	24	no	—
410	C₂×C₄	—	2	24	no	—
411	C₂×C₄	—	2	12	no	—
412	C₂×C₄	—	2	3	no	—
413	C₂×C₄	—	2	12	no	—
414	C₂×C₄	—	2	6	no	—
415	C₂×C₄	—	2	6	no	—
416	C₂×C₄	—	4	3	no	—
417	C₂×C₄	—	4	3	no	—
418	C₂×C₄	C₁₉×#120	1	6	yes	—
419	C₂×C₄	C₂²×D₄×C₁₉	1	3	yes	—
420	C₂×C₄	C₂²×D₄×C₁₉	1	3	yes	—
421	C₈	—	4	1	no	—
422	C₈	—	4	3	no	—
423	C₂²	—	2	6	no	—
424	C₂²	—	2	4	no	—
425	C₂²	—	2	6	no	—
426	C₂²	—	4	1	no	—
427	C₂²	—	4	6	no	—
428	C₂²	—	8	6	no	—
429	C₂²	—	8	3	no	—
430	C₂²	—	8	4	no	—
431	C₂²	—	8	24	no	—
432	C₂²	—	8	12	no	—
433	C₂²	C₂×C₁₉×#120	1	3	yes	—
434	C₄	—	2	6	no	—
435	C₄	—	2	6	no	—
436	C₄	—	8	3	no	—
437	C₄	—	8	1	no	—
438	C₄	C₂×C₁₉×#120	1	3	yes	—
439	C₄	C₂×C₁₉×#120	1	1	yes	characteristic
440	C₂	—	2	3	no	—
441	C₂	—	4	6	no	—
442	C₂	—	4	4	no	—
443	C₂	—	4	6	no	—
444	C₂	C₁₉×#2846	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₉	#2846
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×H(7,𝔽₂)	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
2. C₁₉×#3028	C₂	semidirect
3. C₁₉×#3022	C₂	semidirect
4. C₁₉×#3009	C₂	semidirect
5. C₁₉×#1795	C₂	semidirect
6. C₁₉×#1794	C₂	semidirect
7. C₁₉×#1791	C₂	semidirect
16. C₂×C₁₉×#137	C₂²	semidirect
17. C₂²×SD₁₆×C₁₉	C₂²	semidirect
18. C₁₉×#536	C₂²	semidirect
24. C₁₉×#421	C₂²	semidirect
25. C₁₉×#418	C₂²	semidirect
26. C₁₉×#416	C₂²	semidirect
27. C₁₉×#413	C₂²	semidirect
28. C₁₉×#410	C₂²	semidirect
29. C₁₉×#408	C₂²	semidirect
58. C₂²×Q₈×C₁₉	C₂³	semidirect
70. C₂×M₁₆×C₁₉	C₂³	semidirect
71. C₂²×C₈×C₁₉	C₂³	semidirect
76. C₁₉×#117	C₂³	semidirect
156. #32896	C₁₉	direct (N × H)
202. #3028	C₂×C₁₉	semidirect
203. #3022	C₂×C₁₉	semidirect
204. #3009	C₂×C₁₉	semidirect
205. #1795	C₂×C₁₉	semidirect
206. #1794	C₂×C₁₉	semidirect
207. #1791	C₂×C₁₉	semidirect
233. C₂×#137	C₂²×C₁₉	semidirect
234. C₂²×SD₁₆	C₂²×C₁₉	semidirect
235. #536	C₂²×C₁₉	semidirect
241. #421	C₂²×C₁₉	semidirect
242. #418	C₂²×C₁₉	semidirect
243. #416	C₂²×C₁₉	semidirect
244. #413	C₂²×C₁₉	semidirect
245. #410	C₂²×C₁₉	semidirect
246. #408	C₂²×C₁₉	semidirect
280. C₂²×Q₈	C₂³×C₁₉	semidirect
292. C₂×M₁₆	C₂³×C₁₉	semidirect
293. C₂²×C₈	C₂³×C₁₉	semidirect
298. #117	C₂³×C₁₉	semidirect
307. C₁₉	#32896	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×H(7,𝔽₂)	2
C₁₉×#3028	2
C₁₉×#3022	2
C₁₉×#3009	2
C₁₉×#1795	2
C₁₉×#1794	2
C₁₉×#1791	2
#32896	19

Subgroups — C19×#32896 #18038855

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32896 #18038855